Day 4 Activity Name ___________________________

Solving Systems Using MultiplicationLana did not make 1-point goals, but she made several 2-point and 3-point goals. How many goals of each type did Lana make? In the following exploration, you will write and solve a system of equations to find out the answer.

1. What is the total number of goals that Lana made? Let x represent the number if 2-point goals, and let y represent the number of 3-point goals. Write an equation to describe this situation.

2. How many total points did Lana score? Write an equation using the variables x and y to describe this situation.

3. Model each equation using tiles.

4. Combine your models from Step 3. Was one variable eliminated? Why or why not?

5. Model the equations again, and subtract the terms of the second equation from the terms of the first equation. Was one variable eliminated? Why or why not?

6. How can you use multiplication to change one of the equations so that addition or subtraction will eliminate one of the variables? Multiply each side of the first equation by−2, as shown below. Simplify this equation, and model the equation with tiles.

−2 ( x+ y )=−2(4)

7. Combine the model of the new first equation with the model of the original second equation. What variable is eliminated?

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Day 4 Activity Name ___________________________

8. Solve the system, and check your solution. How many 2-point and 3-point goals did Lana make?

9. Explain why the first equation was multiplied by−2. Could you have eliminated a variable by adding if you had multiplied both sides of the first equation by 2 instead of−2? Explain.

10. What multiplication can you perform in the following system of equations to make elimination by addition possible?

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Day 4 Activity Name ___________________________

Answer Key1. 4 ; x+ y=42. 11;2 x+3 y=113. x+ y=4

2 x+3 y=11

4. No; no neutral pairs were formed.5.

No. After neutral pairs are removed, both x- and y-tiles still remain.6. Multiply one of the equations by a number to create the same or opposite coefficients;

this will eliminate one variable. −2 x−2 y=−8

7.

xis eliminated.

8. (1, 3) Lana made 2-point goal and 3-point goals.9. The first equation was multiplied by −2 to eliminate one of the variables. No; however,

if you multiply by 2 instead of−2, subtraction can be used to eliminate the variablex.

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