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

1. C

2. A

3. D

Step-by-step 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

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus