Question

solve using elimination.
10x + 8y = 14
7x + 8y = -7
(□, □)
submit

Explanation:

Step1: Subtract the two equations

We have the system of equations:

$$\begin{cases} 10x + 8y = 14 \\ 7x + 8y = -7 \end{cases}$$

Subtract the second equation from the first equation to eliminate \(y\):
\((10x + 8y) - (7x + 8y) = 14 - (-7)\)
Simplify the left side: \(10x + 8y - 7x - 8y = 3x\)
Simplify the right side: \(14 + 7 = 21\)
So we get \(3x = 21\)

Step2: Solve for \(x\)

Divide both sides of \(3x = 21\) by 3:
\(x=\frac{21}{3}=7\)

Step3: Substitute \(x = 7\) into one of the original equations to find \(y\)

Let's use the first equation \(10x + 8y = 14\). Substitute \(x = 7\):
\(10\times7 + 8y = 14\)
\(70 + 8y = 14\)
Subtract 70 from both sides:
\(8y = 14 - 70\)
\(8y = -56\)
Divide both sides by 8:
\(y=\frac{-56}{8}=-7\)

Answer:

\((7, -7)\)