The solution to the system is x=−1x, equals, start color blueD, minus, 1, end color blueD, y=1y, equals, start color goldD, 1, end color goldD.
We can check our solution by plugging these values back into the the original equations. Let's try the second equation:
Yes, the solution checks out.
If you feel uncertain why this process works, check out this intro video for an in-depth walkthrough.
We're asked to solve this system of equations:
We can multiply the first equation by −4minus, 4 to get an equivalent equation that has a −16xstart color purpleD, minus, 16, x, end color purpleD term. Our new (but equivalent!) system of equations looks like this:
Adding the equations to eliminate the xx terms, we get:
Solving for yy, we get:
Plugging this value back into our first equation, we solve for the other variable: