Question

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

To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations. (1 point)

Why is this multiplication allowed? (1 point)

What variable will be eliminated when the equations are combined after

the multiplication? (1 point)

Next, add the equations together. Your answer should be a single equation with one variable. (1 point)

Why can you add the equations? (1 point)

Solve the equation for x. (1 point)

Substitute x back into one of the equations to solve for y. (1 point)

What is the solution to the system of equations? (1 point)

Answer 1

Answer:

Step-by-step explanation:

To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations. (1 point)

5x + 2y = 7

6x –2y = 4

Why is this multiplication allowed? (1 point)

Because the entire equation was multiplied by the same number, the equation remains the same.

What variable will be eliminated when the equations are combined after  the multiplication? (1 point)

The Y variable

Next, add the equations together. Your answer should be a single equation with one variable. (1 point)

11x = 11

Solve the equation for x. (1 point)

X = 1

What is the solution to the system of equations? (1 point)

X = 1 and Y = 1 so the answer is (1, 1)

(If you solve this again, but eliminate the X variable, you will still receive that answer 1, so Y = 1)

Answer 2

Sorry my first answer was wrong