Given a system of two equation 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 me why this is true by solving the system of equation given. Justify the reason for each step. HINT: Use addition property of equality and multiplication property of equality in your answer. ( 8 points 5x + 2y = 7
3x - y = 2

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

B) Why is this multiplication allowed?

C) What variable will be eliminated when the equation are combined after the multiplication?

D) Next, add equation together. Your answer should be single equation with one variable.

E) Why can you add the equation?

F) Solve the equation for x.

G) Substitute x back into one of the equation to solve for y.

H) What is the solution to the system of the equation?