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 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
a.
To solve the system using elimination, first multiply the bottom equation by 2. Write
the new system of equations. (1 point)
b. Why is this multiplication allowed? (1 point)
C. What variable will be eliminated when the equations are combined after the
multiplication? (1 point)
D. Next, add the equations together. Your answer should be a single equation with one variable.
E. Why can you add the equations?
F. Solve the equation for x
G. Substitute x back into one of the equations to solve for y
H. What is the solution to the system of equations.