To solve this system of equations, you will need to get one of the terms in both equations to cancel out to zero. If there isn't a term that you can cancel out, you can multiply either or both equations to make that term. There's no wrong way to do this, just as long as you make sure that you double check whether your should add or subtract. This is easier shown than explained, so refer below:
<span> x + y = +1 5x + y = –6
</span>–1(x + y = +1) 5x + y = –6
–x – y = –1 5x + y = –6
You can see that once we combine these equations by adding, the y term will become 0, eliminating it. This is necessary for solving the system, so make sure you do it. Also, remember to distribute the term that you need to to all of the numbers in the equation! After that, just solve for the variable that's still in the equation.
–x – y = –1 + 5x + y = –6
4x + 0y = –7 4x = –7 x = –1.75
Now, just plug the value we found for x into either one of your equations in the original system as it's presented in your problem.
x + y = 1 –1.75 + y = 1 +1.75 +1.75
y = 2.75
All that's left to do is check your point (–1.75, 2.75). If it's true for both equations, your answer is correct!
–1.75 + 2.75 = 1 <span>5(–1.75) + 2.75 = –6
</span>(–1.75, 2.75) is the solution to your system.
