Question

solve the system by the substitution method.
$7x + 9y = -27$
$3x - y = 3$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}. (type an ordered pair.)
b. there are infinitely many solutions.
c. there is no solution.

Explanation:

Step1: Isolate y from second equation

From $3x - y = 3$, rearrange to get $y = 3x - 3$.

Step2: Substitute y into first equation

Substitute $y = 3x - 3$ into $7x + 9y = -27$:
$7x + 9(3x - 3) = -27$
Expand: $7x + 27x - 27 = -27$
Combine like terms: $34x - 27 = -27$

Step3: Solve for x

Add 27 to both sides: $34x = 0$
Solve: $x = \frac{0}{34} = 0$

Step4: Find y using x=0

Substitute $x=0$ into $y = 3x - 3$:
$y = 3(0) - 3 = -3$

Answer:

A. The solution set is $\{(0, -3)\}$.