Question

solve the system by the substitution method.
$x + y = -8$
$y = -3x$

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: Substitute $y=-3x$ into first equation

$x + (-3x) = -8$

Step2: Simplify and solve for $x$

$x - 3x = -8$
$-2x = -8$
$x = \frac{-8}{-2} = 4$

Step3: Substitute $x=4$ into $y=-3x$

$y = -3\times4 = -12$

Answer:

A. The solution set is $\{(4, -12)\}$. (Type an ordered pair.)