Question

How many solutions does this system of equations have?

3x – 4y = 12
y = 4x – 3

A. 0
B. 1
C. 2
D. infinite

Answer 1

B. 1

Explanation:

Since one of the equations is already solved for y, let's use substitution to find out the answer. We will sub in 4x - 3 for y into the first equation:

3x - 4(4x - 3) = 12 and

3x - 16x + 12 = 12 and

-13x = 0 so

x = 0.

Now we will plug in 0 for x into the other equation to solve for y:

y = 4(0) - 3 and

y = 0 -3 so

y = -3

The solution set as a coordinate pair for this system is (0, -3), the only solutiion.