Question

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

{−5x−3y=12y=x−12



Responses

(−6, 6)
begin ordered pair negative 6 comma 6 end ordered pair

(0, −4)
begin ordered pair 0 comma negative 4 end ordered pair

(3, −9)
begin ordered pair 3 comma negative 9 end ordered pair

(1, −11)
begin ordered pair 1 comma negative 11 end ordered pair

Answer 1

To find the solution to the system of equations given by:

1. \( -5x - 3y = 12 \)
2. \( y = x - 12 \)

we can substitute the second equation into the first equation:

1. Substitute \( y \) in the first equation:
\[
-5x - 3(x - 12) = 12
\]

2. Simplify this equation:
\[
-5x - 3x + 36 = 12
\]
\[
-8x + 36 = 12
\]
\[
-8x = 12 - 36
\]
\[
-8x = -24
\]
\[
x = 3
\]

3. Now substitute \( x = 3 \) back into the equation for \( y \):
\[
y = 3 - 12
\]
\[
y = -9
\]

Thus, the solution to the system of equations is \( (3, -9) \).

Now let's check if this ordered pair is one of the choices provided:
- (−6, 6)
- (0, −4)
- (3, −9) **(This is the solution we found)**
- (1, −11)

The correct answer is \((3, -9)\).