Question

How many solutions do each of these systems have ?

1. Y=3/4x-5
-3x+4y=-20

2. X+4y=6
Y=2x-3

3. 6x+3y=-12
Y=-2x+4


1-3 either have
A.One solution
B.two solutions
C.an infinite number
D. No solution

Answer 1

1. C

2. A

3. D

Explanation:

1. The equations will have the same exact line. This is infinite solutions.

-3x + 4y = -20 converts to y = 3/4x - 5

2. To solve the system, substitute y = 2x - 3 into the equation x + 4y = 6.

x + 4(2x-3) = 6

x + 8x - 12 = 6

9x - 12 = 6

9x = 18

x = 2

This system has one solution.

3. The equations will have the same slope. This means no solution is possible.

6x + 3y = -12 converts to y = -2x - 4