Question

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

Answer 1

B. two

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.

Answer 2

B.) two

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