Question

-5x-2y=-20
2x+8y=8
is the answer (-3,4), (-3,-4), (4,0) or (4,3)?

Answer 1

We want to determine -5x-2y=-20 and 2x+8y=8

Simplify the equation for line 1 to get it into our y = mx + b format:
--5x - 2y = -20
-2y = -5x - 20

Divide each side of the equation by -2 to isolate y:
-2y
-2
=

-5x - 20
-2

Simplifying and evaluating, we have:
y = -2.5x + 10
Therefore, the slope of line equation 1 = -2.5

Simplify the equation for line 2 to get it into our y = mx + b format:
2x + 8y = 8
8y = -2x + 8

Divide each side of the equation by 8 to isolate y:
8y
8
=

-2x + 8
8

Simplifying and evaluating, we have:
y = -0.25x + 1
Therefore, the slope of line equation 2 = -0.25

Since y = -2.5x + 10 and y = -0.25x + 1, set each line equation equal to each other and solve for x:
-2.5x + 10 = -0.25x + 1
-2.5x - -0.25x = 1 - 10
- 2.25x = -9
x = -9/ - 2.25
x = 4

Now that we have x, plug it into equation 1 to find y
y = -2.5 * (4) + 10
y = -10 + 10
y = 0
Therefore, our intersection point = (4, 0)

Calculate the product of the 2 slopes:
Slope 1 * Slope 2 = -2.5 * -0.25 = 0.625
Since the product of the 2 slopes <> - 1, the lines are not perpendicular
The 2 lines intersect at (4, 0)