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3. Given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solution. Show why this is true by solving the system of equations given. Justify the reason for each step. HINT: Use the addition property of equality and multiplication property of equality in your answers. (8 points: 1 point for each question) 5x + 2y = 7 3x – y = 2

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Answer: x = 1, y = 1

Step-by-step explanation:

Step 1: Solve for x

Multiply bottom equation by 2.

5x + 2y = 7

2(3x – y = 2)

___________

5x + 2y = 7

+ 6x - 2y = 4

___________

11x =  11    divide each side by 11      x = 1

Step 2: Solve for y

Substitute x=1 into any equation. We will do equation 1.

5x + 2y =  7    5*1 + 2y = 7

5 + 2y = 7  

subtract 5 from each side.

2y = 2  divide each side by 2

y = 1

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