Question

Which ordered pair is the solution to the system of equations? {y=3x−12, 4x+6y=−6)

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

Answer 1

To find the solution to the system of equations, we substitute the ordered pairs (0, -12), (6, -5), (4, -7), and (3, -3) into the equations. The ordered pair that satisfies both equations is (6, -5).

Step-by-step explanation:

To find the solution to the system of equations, we can substitute the given values of x and y into both equations and see which one satisfies both equations. Let's plug in the first ordered pair (0, -12) into the equations:

1. For the first equation, y = 3x - 12, substituting x = 0 and y = -12 gives:

-12 = 3(0) - 12

-12 = -12

This is true, so the first ordered pair (0, -12) satisfies the first equation.

2. For the second equation, 4x + 6y = -6, substituting x = 0 and y = -12 gives:

4(0) + 6(-12) = -6

-72 = -6

This is not true, so the first ordered pair (0, -12) does not satisfy the second equation.

Therefore, the ordered pair (0, -12) is not the solution to the system of equations.

We need to check the other options to find the correct solution.

Let's substitute the second ordered pair (6, -5) into the equations:

1. For the first equation, y = 3x - 12, substituting x = 6 and y = -5 gives:

-5 = 3(6) - 12

-5 = 18 - 12

-5 = 6

This is not true, so the second ordered pair (6, -5) does not satisfy the first equation.

2. For the second equation, 4x + 6y = -6, substituting x = 6 and y = -5 gives:

4(6) + 6(-5) = -6

24 - 30 = -6

-6 = -6

This is true, so the second ordered pair (6, -5) satisfies the second equation.

Therefore, the ordered pair (6, -5) is the solution to the system of equations.