Question

solve the following system using the elimination method. enter your answer as an ordered pair in the form $(x,y)$ if there is one, unique solution. enter all if there are infinitely many solutions and enter none if there are no solutions.
$\

$$\begin{cases}5x + 4y = -24\\\\-5x - 3y = 18\\end{cases}$$

$

Explanation:

Step1: Add the two equations

$$(5x + 4y) + (-5x - 3y) = -24 + 18$$
Simplify: $y = -6$

Step2: Substitute $y=-6$ into first equation

$$5x + 4(-6) = -24$$
Simplify: $5x - 24 = -24$

Step3: Solve for $x$

$$5x = -24 + 24$$
$$5x = 0$$
$$x = 0$$

Answer:

$(0, -6)$