Question

How many solutions does this linear system have?

Answer 1

If you would like to solve the system of equations, you can do this using the following steps:

y = 2x - 5
-8x - 4y = -20
___________
-8x - 4y = -20
-8x - 4 * (2x - 5) = -20
-8x - 8x + 20 = -20
20 + 20 = 16x
16x = 40
x = 40/16
x = 2.5

y = 2x - 5 = 2 * 2.5 - 5 = 5 - 5 = 0

(x, y) = (2.5, 0)

The correct result would be: b. one solution: (2.5, 0).

Answer 2

B. One solution: (2.5, 0)

Substitute the first equation to the second equation to find for X:
-8X - 4 (2X - 5) = -20.
Multiplying 4 (2X - 5) will give you (8X - 20).

The equation will now be:
-8X - (8X - 20) = -20 or -8X - 8X +20 = -20
-16X = -20 -20
-16X = -40
X = 2.5


To get Y, substitute the answer that we got from X to the first equation:
Y = 2 (2.5) - 5
Y = 5 - 5
Y = 0