Question

1. 10x + 2y = 18

10x - 7y = -18

Explanation:

Step1: Subtract the two equations to eliminate \(x\)

We have the system of equations:
\[

$$\begin{cases} 10x + 2y = 18 \\ 10x - 7y = -18 \end{cases}$$

\]
Subtract the second equation from the first equation:
\[
(10x + 2y) - (10x - 7y) = 18 - (-18)
\]
Simplify the left - hand side: \(10x+2y - 10x + 7y=9y\)
Simplify the right - hand side: \(18 + 18 = 36\)
So we get the equation \(9y=36\)

Step2: Solve for \(y\)

From \(9y = 36\), divide both sides by 9:
\(y=\frac{36}{9}=4\)

Step3: Substitute \(y = 4\) into one of the original equations to solve for \(x\)

Substitute \(y = 4\) into the first equation \(10x+2y = 18\):
\(10x+2\times4=18\)
\(10x + 8 = 18\)
Subtract 8 from both sides: \(10x=18 - 8=10\)
Divide both sides by 10: \(x = 1\)

Answer:

\(x = 1,y = 4\)