Solving systems of equations by substitution guided notes answers

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# Solving systems of equations by substitution guided notes answers

In order to keep us on schedule, a hint was provided for today's Do-Now with respect to the new procedure, Elimination. After five minutes I will ask two students to come up to the board to show their answers to the class. I will ask that each student solve the system using a different method. After they finish, I will ask the class to analyze their work to see if the students arrived at the same answer. Before moving on, I will ask students to summarize what we learned about elimination during yesterday's class.

Before moving forward, I will return the graded Exit Cards to students from our last class. We will review the responses as a whole group. This activity was designed to address two misconceptions that students commonly possess when they begin to solve systems of equations with elimination. One goal of this activity is for students to discover that the value of a solution doesn't change when the entire equation is multiplied by a scale factor.

The second aim is for students to understand that this congruence only exists when ALL terms are multiplied by the same scale factor. After 5 minutes we will reconvene as a whole class to have a discussion about our responses.

I will ask students to brainstorm how scaling an equation could be advantageous to an Algebra student. Students will copy the text below on their notes:. I will ask students to solve Example One with elimination without encouraging them to scale one of the equations. I expect that my students will be quick to see that nothing will eliminate with addition, or even when the signs are changed in one equation. Next, I will ask students to recall what we discovered in our Elimination Investigation.

I will tell students that we can use that the procedure that was completed during the Investigation to alter one equation in a system so that the coefficients form a zero pair. For example, if we examine both sets of variables, 5y and -3y have nothing in common but -3x and 6x do. If we multiply the top equation by two, we will have created a zero pair. After multiplying the top equation by 2, we will finish solving the system.

We will then solve Example Two and the You Try problems. Examples Three and Four contain the same system of equations. Students will organize the cards into groups of three original system, scale factor, solution. I will observe my students as they work looking to see if students:. I will ask a volunteer to summarize what we did in class today. Then, I will ask the class to reflect upon the importance of knowing how to solve a system using three different methods.

I will ask them to justify their reasoning. Empty Layer. Home Professional Learning. Professional Learning. Learn more about. Sign Up Log In. Algebra I Noelani Davis. Unit 6 Unit 1: Welcome Back! SWBAT solve systems of equations using elimination. Big Idea Students will investigate properties of equality with scaled numbers. Students will use multiplication to create zero pair coefficients. Lesson Author. Grade Level. Systems of Equations and Inequalities.After 5 minutes, I will ask student volunteers to come to the front of the room to show their answers on the board.

I will ask the class to define "substitution", and to give some real world examples of when a substitution would be made. Students will complete the "Math Lib" on S l ide Two of today's presentation. The purpose of this activity is for students to make a connection between equality and idea of one thing representing another. Students will create their own unique list on the back of their Do-Now sheet, using the criteria on the board.

Next, I will tell students to turn and talk with the people sitting around them, sharing their version of the story with their set of words inserted. I will also ask a few volunteers to share their story aloud for the class. Before moving on, I will ask the students to hypothesize why they think I chose to have them complete a Math Lib, when today's objective is to solve a linear system with substitution.

The video below shows how I will present these ideas in front of the class:. Unable to display content. Adobe Flash is required. I will ask students to use the rest of class to practice solving systems of equations using substitution. Today, I will ask students to use a TI-Inspire calculator to check solutions as they move along on the handout. I will ask students to complete two to three problems at a time, then to stop to check their solution in the calculator before moving forward to the next one.

If their solution does not match with the calculators, I will ask students to work in a pair with me or another student to help get them back on the right track. I will ask the students to describe how the computer phrase "copy and paste" would be a great analogy to describe solving a system with substitution.

Algebra I Noelani Davis. Unit 6 Unit 1: Welcome Back! Students will solve linear systems of equations using substitution.In some word problems, we may need to translate the sentences into more than one equation. If we have two unknown variables then we would need at least two equations to solve the variable.

In general, if we have n unknown variables then we would need at least n equations to solve the variable. In the Substitution Method, we isolate one of the variables in one of the equations and substitute the results in the other equation.

We usually try to choose the equation where the coefficient of a variable is 1 and isolate that variable. This is to avoid dealing with fractions whenever possible. If none of the variables has a coefficient of 1 then you may want to consider the Addition Method or Elimination Method. Steps to solving Systems of Equations by Substitution: 1.

Isolate a variable in one of the equations. Substitute the isolated variable in the other equation. This will result in an equation with one variable. Solve the equation. Substitute the solution from step 3 into another equation to solve for the other variable. Recommended: Check the solution. Step 1: Try to choose the equation where the coefficient of a variable is 1. Step 2: From equation 3we know that y is the same as 3 x - 8. Step 3: Remove brackets using distributive property. Step 4: Combine like terms. Step 5: Isolate variable x. Step 7: Check your answer with equation 1. Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. Related Topics: Worksheets to practice solving systems of equations More Algebra Lessons These algebra lessons introduce the technique of solving systems of equations by substitution.

The following example show the steps to solve a system of equations using the substitution method. Scroll down the page for more examples and solutions. You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics.Teaching systems of equations is always a challenge for me. We use the interactive notebook throughout the unit.

We add information, synthesize, practice, and reflect, all in the interactive notebook. You can choose the ones that work for you and your students. Then, we look back at them through out the unit. Students can look at this and reflect to themselves on whether or not they understand how to solve a system of equations with substitution and so forth. When it comes times for the test, I have students write a reflection about how their learning has progressed. I like to to give them sentence stems to make their answers better. After the I Can Statements, I like to add a vocabulary or building background activity. This is a type of warm-up for the whole unit. With this background building activity for working with systems of equations, I let students try to complete whatever they can on their own. If they need more help then I describe the different types of solving methods and let them write some things down.

As another option, you could have the students interview you and ask the teacher questions to try and figure out the answers. This activity gives you a chance to see who has a background with the topic. Also, students get a chance to talk about and write about systems of equations. To take notes on how to solve systems of equations, I use a foldable graphic organizer for each approach.

### Solving Systems of Equations by Elimination - Guided Notes and Homework

The goal of this note-taking is to help students learn each process. The foldable that we use can be seen below. On the inside students work through a problem and have an example to refer to during practice.

We use a different foldable and a different set of steps when it comes to solving a system of equations using substitution:. You have to be careful to not emphasize the words. Students really need to see the process. This should be encouraged. Graphing to solve a system of equations brings together so many of the concepts and skills that we teach in 8th grade and Algebra I. When we teach students all of the different methods, ultimately they have to learn when each one is appropriate.

They have to choose whether to solve with substitution, elimination, or graphing. Here are the steps for solving a system of equations by graphing:. The foldable that I use to teach about solving systems of equations through graphing walks students through one example. Later, you have to keep reminding students to go back to the notes and look at the worked example when they get stuck.

Another part of this standard is for students to identify how many solutions a system of equations has. It presents a series of if-then statements that lead students to the answer.

## Solving Linear Systems of Equations with Substitution (Day 1 of 3)

On the inside of the foldable it has a place where students can draw an example and explain why. For some students who need more support I print this foldable with example already there. Due to the difficulty of this topic, I try to introduce one of the methods for solving at a time. I have two pages that I work with to do guided practice.What software do you use to create your guided notes? I really like this idea,but don't know how to make my documents look as professional as yours.

Thank You I create all of my guided notes in Microsoft Word. It's super easy for me because I have been using Word for years. I love the format and layout of your INB pages. Are these available for download or purchase somewhere? I will update my store this summer I decided to change how I paced and taught my Systems of Equations Unit. This year in my Linear Relationships in Situations Unit I set up the foundation for using slope-intercept form in situations.

I taught the students how to represent situations with an equation, on a graph and with a table. And I taught the students that the best method for solving problems using slope-intercept form was algebraically with the equation. This foundation helped the students to be successful in solving Systems of Equations in Situations. Solving Systems of Equations by Graphing - 2 Weeks. Here is my Socrative Code. Feel Free to Use.

Solving Systems Using Elimination - 3 Weeks. This was by far one of my Socrative lessons that I created. The students loved making the review posters and it really helped solidify the concept of elimination word problems. Solutions to Systems of Equations 2 Days. Email This BlogThis! Labels: My Math 8 Units.

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Donate Login Sign up Search for courses, skills, and videos. Math Algebra I Systems of equations Solving systems of equations with substitution.

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Systems of equations with substitution: potato chips. Practice: Systems of equations with substitution. Substitution method review systems of equations.

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Next lesson. Current timeTotal duration CCSS Math: 8. Google Classroom Facebook Twitter. Video transcript So that it's less likely that we get shown up by talking birds in the future, we've set a little bit of exercise for solving systems of equations with substitution. And so this is the first exercise or the first problem that they give us.

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We can take this constraint, the constraint on y in terms of x and substitute it for y in this first blue equation and then solve for x.

So let's try it out. So this first blue equation would then become -3x-4 but instead of putting a y there the second constraint tells us that y needs to be equal to 2x So it's 4 2x-5 and all of that is going to be equal to So now we get just one equation with one unknown. So, let's see if we can do that.Index of lessons Print this page print-friendly version Find local tutors.

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Solving Systems by Substitution. The method of solving "by substitution" works by solving one of the equations you choose which one for one of the variables you choose which oneand then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other.

Then you back-solve for the first variable. Here is how it works. I'll use the same systems as were in a previous page. The idea here is to solve one of the equations for one of the variables, and plug this into the other equation.

It does not matter which equation or which variable you pick. There is no right or wrong choice; the answer will be the same, regardless. But — some choices may be better than others.

It wouldn't be "wrong" to make a different choice, but it would probably be more difficult. Being lazy, I'll solve the second equation for y :. Now I'll plug this in "substitute it" for " y " in the first equation, and solve for x :.

Now I can plug this x -value back into either equation, and solve for y. Twenty-four does equal twenty-four, but who cares? So when using substitution, make sure you substitute into the other equation, or you'll just be wasting your time.

We already know from the previous lesson that these equations are actually both the same line; that is, this is a dependent system.

We know what this looks like graphically: we get two identical line equations, and a graph with just one line displayed. But what does this look like algebraically? The first equation is already solved for yso I'll substitute that into the second equation:.

Well, um I did substitute the first equation into the second equation, so this unhelpful result is not because of some screw-up on my part. It's just that this is what a dependent system looks like when you try to find a solution. Remember that, when you're trying to solve a system, you're trying to use the second equation to narrow down the choices of points on the first equation.

You're trying to find the one single point that works in both equations. 