How many solutions does this system of equations have?

3x = - 12y+15 and x+4y=5

A. one

B. two

C. infintely many

D. none

B. two

Step-by-step explanation:

3x = - 12y + 15 x + 4y = 5

Use the elimination method to solve the system of equations. Move the terms like so. As you can see I kept the first equation the same but multiplied the second equation by - 3.

3x = - 12y + 15 - 3x = - 12y - 15

Now add. 3x and - 3x cancel; so does 15 and - 15.

0 = - 24y

Divide by - 24. 0 div'd by - 24 is equal to 0.

y = 0

Substitute y into the second equation.

x + 4 (0) = 5

x + 0 = 5

x = 5

You've got x = 5 and y = 0; these are two solutions to the system of equations.

B.) two

Step-by-step explanation:

These equations have two solutions, one for solving for each variable. There is a solution for solving for x, and one for y. For both of these equations,

x = 5 - 4y and y = 5/4 - x/4