Kaitlin,
Put your "system of equations" hat on your head so that you can solve this problem.
–5x + y = –3
3x – 8y = 24
If I can figure out what x equals or what y equals, then I can put the equivalent expression for x or y into the other equation and solve it for the single unknown.
If I rewrite the first equation, I can get:
y = –3 + 5x
Now I have an expression (–3 + 5x) that is equal to y. So I will substitute this expression for y in the second equation above.
3x – 8y = 24
3x – 8(–3 + 5x) = 24
3x + 24 – 40x = 24
–37x = 0
x = 0
Now I will put this value for x into the first equation that we were originally given and solve for y.
x = 0
–5x + y = –3
–5(0) + y = –3
0 + y = –3
y = –3
This tells us that the two equations that were given, which represent lines in a plane, intersect at the point (0,–3). Another way to say this is that x = 0 and y = –3 make both equations true.
Let's check this.
–5x + y = –3 => –5(0) + (–3) = –3 => 0 – 3 = –3 => –3 = –3 TRUE
3x – 8y = 24 => 3(0) – 8(–3) = 24 => 0 + 24 = 24 => 24 = 24 TRUE
