how do i graph an equation like -5x+y=-3 and 3x-8y=24 to find the point of intersection between them
-5x + y = 3
Add 5x to both sides
-5x + y + 5x = 3 + 5x
so y = 3 + 5x as the 5x's on the left-hand side cancel each other out.
3x - 8y = 24
Add 8y to both sides
3x - 8y + 8y = 24 + 8y
so 3x = 24 + 8y
Subtract 24 from both sides
3x - 24 = 24 + 8y - 24
so 3x - 24 = 8y
Divide all terms by 8
3x/8 - 24/8 = 8y/8
so 3x/8 - 3 = y (or y = 3x/8 - 3)
.
Rearrange them to get them in the following forms:
y = 5x + 3
and
y = (3/8)x - 3
.
-5x + y = 3
Add 5x to both sides
-5x + y + 5x = 3 + 5x
so y = 3 + 5x as the 5x's on the left-hand side cancel each other out.
3x - 8y = 24
Add 8y to both sides
3x - 8y + 8y = 24 + 8y
so 3x = 24 + 8y
Subtract 24 from both sides
3x - 24 = 24 + 8y - 24
so 3x - 24 = 8y
Divide all terms by 8
3x/8 - 24/8 = 8y/8
so 3x/8 - 3 = y (or y = 3x/8 - 3)
.