Question

Which ordered pair is the solution to the system of equations? {y=3x−124x+6y=−6 (3, −3) (6, −5) (0, −12) (4, −7)

Answer 1

Option A is correct.

The only ordered pair which is the solution to the system of equations is ; (3, -3)

Explanation:

Given the system of equation:

y = 3x - 12 ......[1]

4x + 6y = -6 ......[2]

Substitute equation [1] in [2] we have;

`4x + 6 (3x - 12) = -6`

Using distributive property :
`a \cdot (b+c) = a \cdot b + a \cdot c`

4x + 18x - 72 = -6

Combine like terms;

22x - 72 = -6

Add 72 to both sides of an equation; we get

22x - 72 + 72 = -6 + 72

Simplify:

22x = 66

Divide by 22 to both sides we get;

`(22x)/(22) = (66)/(22)`

Simplify:

x = 3

Substitute the value of x = 3 in equation [1] to solve for y;

y = 3(3) - 12

y = 9 - 12= -3 or

y = -3

Therefore, the only ordered pair (x, y) the solution of the system of equation is ( 3, - 3).