Question

solve the system by elimination. -8x - 10y = 20 -8x - 6y = -4 (6, 5) (5, -6) (-6, -5) infinite number of solutions

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases}-8x - 10y = 20 \\ -8x - 6y = -4\end{cases}$$

Subtract the second equation from the first equation:
$$(-8x - 10y)-(-8x - 6y)=20-(-4)$$
Simplify the left side: $-8x - 10y + 8x + 6y=-4y$
Simplify the right side: $20 + 4 = 24$
So we get $-4y=24$

Step2: Solve for y

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

Step3: Substitute y into one of the equations

Substitute $y = - 6$ into the second equation $-8x-6y=-4$:
$$-8x-6\times(-6)=-4$$
Simplify: $-8x + 36=-4$

Step4: Solve for x

Subtract 36 from both sides:
$$-8x=-4 - 36=-40$$
Divide both sides by $-8$:
$$x=\frac{-40}{-8}=5$$

Answer:

$(5, - 6)$