Question

A system of equations is given below.

2x + 7y = 1
-3x – 4y = 5

Create an equivalent system of equations by replacing the first equation by multiplying the first equation by an integer other than 1, and adding it to the second equation.

Use any method to solve the equivalent system of equations (the new first equation with the original second equation).


Prove that the solution for the equivalent system is the same as the solution for the original system of equations

Answer 1

First, solve the given system of linear equations.

Second, multiply the first equation by 4 (which was an arbitrary choice). Add your result to the 2nd equation.

You should now have the following:

First equation: No change: 2x + 7y = 1

Second equation: 4(-3x – 4y = 5) = -12x -16y = 20

Solve this new system of linear equations. Do you (or do you not) obtain the same solution as your earlier one?