Question

Which ordered pair is the solution to the system of equations?

{−5x−3y=12y=x−12



A(0, −4)

B(−6, 6)

C(3, −9)

D(1, −11)

Answer 1

The answer is C(3, -9)

Answer 2

Option C is correct

The ordered pair which is the solution of the system of given equations is (3, -9)

Explanation:

Given the system of equation:

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

-5x - 3y =12 ......[2]

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

`-5x-3(x-12)=12`

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

-5x - 3x+36 = 12

Combine like terms;

-8x +36 = 12

Subtract 36 to both sides of an equation; we get

-8x +36 -36 = 12 -36

Simplify:

-8x = -24

Divide by -8 to both sides we get;

`(-8x)/(-8) =(-24)/(-8)`

Simplify:

x = 3

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

y = 3 -12 = -9

or y = -9

Therefore, the only ordered pair (x, y) the solution of the system of equation is ( 3, -9).