Question

solving systems multiplication
solve each system by elimination.

1. $-4x + 8y = -16$

$-6x - 4y = 8$

Explanation:

Step1: Eliminate $y$ variable

Multiply the second equation by 2:
$$2\times(-6x - 4y) = 2\times8 \implies -12x - 8y = 16$$

Step2: Add to first equation

Add the new equation to the first equation to eliminate $y$:
$$(-4x + 8y) + (-12x - 8y) = -16 + 16$$
$$-16x = 0$$

Step3: Solve for $x$

Divide both sides by $-16$:
$$x = \frac{0}{-16} = 0$$

Step4: Substitute $x=0$ into second equation

Use the original second equation to find $y$:
$$-6(0) - 4y = 8 \implies -4y = 8$$

Step5: Solve for $y$

Divide both sides by $-4$:
$$y = \frac{8}{-4} = -2$$

Answer:

$x=0$, $y=-2$