Question

Find the solution to the following system of equations using any method: 4x - y = 3 -4x + y = -3

Answer 1

Start by writing out the system of equations.

• 4x - y = 3
• -4x + y = -3

The easiest way to solve this system of equations is the elimination method. This is because both equations contain opposites of each other that you can cancel out.

Add the system of equations together. After adding, everything cancels out. 4x + (-4x) = 0 ; -y + y = 0 ; 3 + (-3) = 0.

You are left with the equation of 0 = 0. Since this is a TRUE statement, this means that there are infinitely many solutions to this system of equations.

If you were left with a false statement, for example 4 = 0, then the answer would be "no solution".