Question

what is the solution to this system of linear equations?
y=-6x+52
y=2x+17

Answer 1

Well there are multiple ways of solving this system of equations. The one I'm going to use in this case will be to just set them equal to each other.
y=-6x+52
y=2x+17 (tip is to think that y is the same thing as y. Like an apple is the same thing as an apple. So if y equals both of those, then when you finally get x, they'll end up being the same thing.)
2x+17=-6x+52 (then just solve for x)
+6x +6x
8x+17=52
-17 -17
8x=35
/8 /8
x=4.375
From here, to find y, just plug the solution for x into one of your equations. I'm just going to do y=2x+17 because it's a little easier than the other.
y=2x+17
y=2(4.375)+17
y=8.75+17
y=25.75
Not the prettiest number, but let's check now by plugging in both the solutions for x and y into one of the equations just to make sure. This time I'll just go with the first equation... just because I did the second one last time. I'm trying to spice it up here.
y=-6x+52
25.75=-6(4.375)+52
25.75=-26.25+52
25.75=25.75
Yeah! We did it!!
So your answer is...
y=25.75
x=4.375
but your teacher will probably want you to write it as...
(4.375, 25.75)