Question

solve this system of equations by using elimination. \\(\

$$\begin{cases} x + 4y = -17 \\\\ 2x - 2y = 16 \\end{cases}$$

\\) \\((?, )\\)

Explanation:

Step1: Scale second equation to eliminate y

Multiply the second equation by 2:
$$2\times(2x - 2y) = 2\times16$$
$$4x - 4y = 32$$

Step2: Add to first equation

Add the scaled equation to the first equation to eliminate $y$:
$$(x + 4y) + (4x - 4y) = -17 + 32$$
$$5x = 15$$

Step3: Solve for x

Divide both sides by 5:
$$x = \frac{15}{5} = 3$$

Step4: Substitute x into first equation

Plug $x=3$ into $x + 4y = -17$:
$$3 + 4y = -17$$

Step5: Solve for y

Subtract 3 from both sides, then divide by 4:
$$4y = -17 - 3 = -20$$
$$y = \frac{-20}{4} = -5$$

Answer:

$(3, -5)$