Question

solve using elimination.
2x - 10y = -12
8x - 10y = 12

Explanation:

Step1: Subtract the two equations

We have the system of equations:

$$\begin{cases} 2x - 10y = -12 \\ 8x - 10y = 12 \end{cases}$$

Subtract the first equation from the second equation:
$$(8x - 10y)-(2x - 10y)=12-(-12)$$
Simplify the left side: $8x - 10y - 2x + 10y = 6x$
Simplify the right side: $12 + 12 = 24$
So we get $6x = 24$

Step2: Solve for x

Divide both sides of $6x = 24$ by 6:
$$x=\frac{24}{6}=4$$

Step3: Substitute x into one equation to find y

Substitute $x = 4$ into the first equation $2x - 10y = -12$:
$$2(4)-10y=-12$$
Simplify: $8 - 10y = -12$
Subtract 8 from both sides: $-10y=-12 - 8=-20$
Divide both sides by -10: $y=\frac{-20}{-10}=2$

Answer:

$(4, 2)$