Question

a system of equations is given.\

$$\begin{cases}5x + 16y = 40\\\\-3x - 8y = -24\\end{cases}$$

\
what is the solution to this system of equations? enter a number in each box.\
$(x, y) = (\square, \square)$

Explanation:

Step1: Eliminate y by scaling eq2

Multiply the second equation by 2:
$$2(-3x - 8y) = 2(-24) \implies -6x - 16y = -48$$

Step2: Add to first equation

Add the new equation to the first equation to eliminate $y$:
$$(5x + 16y) + (-6x - 16y) = 40 + (-48)$$
$$-x = -8$$

Step3: Solve for x

Multiply both sides by -1:
$$x = 8$$

Step4: Substitute x into eq2

Plug $x=8$ into $-3x -8y = -24$:
$$-3(8) -8y = -24 \implies -24 -8y = -24$$

Step5: Solve for y

Isolate $y$:
$$-8y = -24 + 24 \implies -8y = 0 \implies y = 0$$

Answer:

$(x, y) = (8, 0)$