Question

Which ordered pair is the solution to the system of equations y = 3x - 12 and 4x - 6y = -6?

a. (3, -3)
b. (4, -7)
c. (6, -5)
d. (0, -12)

Answer 1

The solution to the system of equations y = 3x - 12 and 4x - 6y = -6 is (6, 6).

Step-by-step explanation:

To find the solution to the system of equations y = 3x - 12 and 4x - 6y = -6, we can solve the equations simultaneously by substitution or elimination.

Let's use substitution. We'll solve the first equation for y:

y = 3x - 12.

Now substitute this expression for y into the second equation:

4x - 6(3x - 12) = -6.

Simplify the equation:

4x - 18x + 72 = -6.

-14x + 72 = -6.

-14x = -78.

x = -78 / -14 = 6.

Now substitute the value of x back into the first equation to find y:

y = 3(6) - 12.

y = 18 - 12 = 6.

So, the solution to the system of equations is (6, 6).