Question

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

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

Answer 1

To find the solution to the system of equations y = 3x - 12 and 4x - 6y = -6, we can use the elimination method. By adding the two equations together, we eliminate the y terms and solve for x. Then, substitute the value of x into one of the original equations to find y. The solution is (11/3, -1).

Step-by-step explanation:

To find the solution to the system of equations y = 3x - 12 and 4x - 6y = -6, we need to find the values of x and y that satisfy both equations. We can do this by either substitution or elimination. Let's use elimination method.

1. Multiply the first equation by 2 so that the coefficient of y becomes -12 in both equations: 2y = 6x - 24
2. Rearrange the second equation: 4x + 6y = -6
3. Add the two equations together to eliminate the y terms: 2y + 6y = 6x - 24 + (-6)
4. Simplify: 8y = 6x - 30
5. Divide both sides of the equation by 8: y = (6/8)x - (30/8)
6. Simplify further: y = (3/4)x - (15/4)
7. Substitute the value of y into one of the original equations: (3/4)x - (15/4) = 3x - 12
8. Multiply both sides of the equation by 4 to get rid of the fractions: 3x - 15 = 12x - 48
9. Subtract 3x from both sides: -15 = 9x - 48
10. Add 48 to both sides: 33 = 9x
11. Divide both sides by 9: x = 33/9
12. Simplify: x = 11/3

Now substitute the value of x into one of the original equations to find y: y = 3(11/3) - 12 = 11 - 12 = -1

Therefore, the ordered pair (11/3, -1) is the solution to the system of equations.