# Lesson 16 solve systems of equations algebraically answer key

This low-prep activity is an engaging way for students to practice working with systems of equations! Students become suspects after a hotel staff member is murdered. The murderer left a cluesheet and students must work together, solving the systems of equations problems on the cluesheet to figure out who the murderer is! The clue sheet includes a variety of problems, including solving systems from word problems, solving by graphing, matrices, and substitution.

Students are given character cards when they enter the room and assume the role of a bus passenger. Their leisurely trip is brought to a sudden halt when one of the passengers is found dead. This product is aligned to CCSS 8.

Murder Mystery! Solving Equations Mystery! Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials.

## Solve Systems of Equations by Graphing (Lesson Plan with Homework)

Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? All Categories. Grade Level. Resource Type. Log In Join Us. View Wish List View Cart. Systems of Equations Activity! Mini Mystery.

View Preview. MathAlgebra. Grade Levels. ActivitiesFun StuffGames. File Type. CCSS 8. Also included in:. CCSS Aligned! View Bundle. Algebra 1 Activities Bundle! This Algebra I activity bundle will keep your students engaged throughout the year with 7 Mystery Activities! Product Description Standards NEW This low-prep activity is an engaging way for students to practice working with systems of equations!

Log in to see state-specific standards only available in the US. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.By Mary Jane Sterling.

## Solving Systems of Equations

A solution of a system of two linear equations consists of the values of x and y that make both of the equations true — at the same time. Graphically, the solution is the point where the two lines intersect. The two most frequently used methods for solving systems of linear equations are elimination and substitution:.

Elimination also called add-subtract : This method involves adding the two equations together — or multiples of the two equations — so that in the sum, the coefficient of one of the variables becomes 0. That variable drops out is eliminatedso you can solve for the other variable.

Then you plug the solution back into one of the original equations and solve for the variable you eliminated. Substitution: This method has you set one of the equations equal to x or y. You can then substitute the equivalent of the variable from one equation for that variable into the other equation. You end up with a single-variable equation, which you can solve. Then plug that answer into one of the original equations and solve for the other variable.

You can use either method to solve linear systems, and you choose one over the other if a method seems to work better in a particular system substitution works best if the coefficient on one of the variables is 1 or —1.

The following examples show the same system of equations solved using both methods. You choose the number —2 as a multiplier because it makes the coefficient of the x term in the first equation equal to —2, while the coefficient on x in the second equation is 2.

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The numbers —2 and 2 are opposites, so adding the equations together eliminates the x term:. You can also solve for the x -value by putting the 3 into the second equation — you get the same result. To use substitution, select a variable in one of the equations with a coefficient of 1 or —1.

The only variable that qualifies in this system is x in the first equation. Solve for x in terms of y in that equation. Substitute that equivalent of x into the second equation. That answer should look familiar. Multiply the terms in the first equation by 2 and the terms in the second equation by 3.

As a result, you end up adding —6 y and 6 y together, which eliminates the y terms when you add the two equations. The second equation is already solved for y. Solving Two Linear Equations Algebraically.Solve systems of linear equations using substitution when one equation is already solved for a variable. Turn content from Match Fishtank lessons into custom handouts for students in just a few clicks.

Download Sample. The essential concepts students need to demonstrate or understand to achieve the lesson objective. Understand substitution as an algebraic approach to solving a system of equations. Understand that the method of substitution replaces one of the variables in the system with an expression in order to solve for the remaining variable. Look for and make use of the structure of equations in a system to identify which expression to substitute into which equation MP. Use substitution to solve systems of equations.

This is the first of three lessons on substitution. In Lesson 5, students focus on the concepts behind substitution and why it works. In Lesson 6, students will solve an equation first before substituting, and they will look at examples with no or infinite solutions. Finally in Lesson 7, students will apply this strategy of solving systems to real-world applications. Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding.

Before you substitute, how many variables do you have? Can you solve for the value of either variable when you have two unknowns? Can you solve for the value of the single unknown? This Anchor Problem introduces students to the idea of using substitution to create a single-variable equation that can be solved. Students are familiar with substituting numerical values in for variables; in this Anchor Problem, they extend on that idea to substitute in an algebraic expression.

Solve the system below using substitution. Write your final answer as a coordinate point.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.

Simultaneous Equations Math Lesson

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.

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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. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.Learn Zillion Instructional Videos. Graphing to solve systems of equations 8.

Solve pairs of simultaneous linear equations; understand why solutions correspond to points of intersection 8. Analyze and solve pairs of simultaneous linear equations; solve systems in two equations algebraically 8. Guided Practice. IXL Lessons.

Make sure you sign-in at the IXL website prior to clicking the specific lessons. Link to sign-in. Ready Common Core. Search this site. Grade 5. Grade 6. Grade 7.

### Systems of Linear Equations

Grade 8. Student Book pages - C Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Learn Zillion Instructional Videos Graphing to solve systems of equations 8.

Interactive Manipulatives. Click "Select Grade" to enter 8th Grade Click "Backgrounds" if you want to have a graphic organizer in the background. Optional Click "Manipulatives" to select the type of manipulatives. Solve a system of equations by graphing: word problems Eighth grade - Y.Today we are going to extend solving systems of linear equations to non-linear equations.

I begin the lesson by giving students a linear system solve.

### Solving Systems of Equations by Substitution

As students work I identify the methods used by students. Most students either rearrange the equations to put the equations into a calculator or solve by elimination also called linear combination. After a few minutes I have students share their process in solving. I give students the names of the 3 methods learned in Algebra 1 and 2. Namely elimination, graphing and substitution.

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I ask students to identify which process is demonstrated on the board. Since I rarely have students who do substitution on this problem we go through the substitution method on the problem. I ask students why substitution is not the most efficient method for this system. Now that we have reviewed solving systems I give students a problem with one equation being non linear. I ask students to decide how they can solve the problem. Students discuss ideas with each other and some start to work on the problem. After a couple of minutes I have students share ideas.

Some solve the second equation for y and then substitute. Other try elimination by subtracting the second equation from the first. Students that have started working the problem put their process on the board for discussion. To help students see how the graphs intersect, I graph page 2 the functions in Desmos. Desmos allows the equations to be typed without rearranging which helps in the class.

We identify the points of intersection and use the graphs to verify what happens in the algebra.Empty Layer. Building Functions. Trigonometric Functions. HS Geometry Congruence. Expressing Geometric Properties with Equations. Modeling with Geometry.

Using Probability to Make Decisions. Eighth Grade. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

Big Idea: Students will identify zero pair coefficients to solve systems of equations by adding. Standards 8.

Big Idea: Students move about in a scavenger hunt, solving systems using different algebraic methods. Big Idea: Students use data to create equations describing a concrete scenario.

Students analyze the equations as a system to solve a problem. Big Idea: Assess what students have learned about systems, and find where they may still need help conceptually. Elimination 1 - add or subtract only 8th Grade Math. Big Idea: Why does elimination work? Use sensitive nieces, peppermint bark, and gingerbread men to illustrate this mathematical concept.

Baseball Helmets Day 1 of 2 8th Grade Math. Big Idea: Connect solving systems of equations to real life baseball helmets and reading tables to find the equations for solving by substitution. Elimination 4 - multiply one equation only 8th Grade Math. Big Idea: More practice!

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Get kids fluent in solving systems using elimination