Question

1. 9x + 8y = 22

9x + 6y = 21

Explanation:

Step1: Subtract the two equations

Subtract the second equation \(9x + 6y = 21\) from the first equation \(9x + 8y = 22\) to eliminate \(x\).
\[

$$\begin{align*} (9x + 8y) - (9x + 6y) &= 22 - 21\\ 9x + 8y - 9x - 6y &= 1\\ 2y &= 1 \end{align*}$$

\]

Step2: Solve for \(y\)

Divide both sides of the equation \(2y = 1\) by 2.
\[
y=\frac{1}{2}
\]

Step3: Substitute \(y\) into one of the original equations

Substitute \(y = \frac{1}{2}\) into the first original equation \(9x + 8y = 22\).
\[

$$\begin{align*} 9x + 8\times\frac{1}{2}&=22\\ 9x + 4 &= 22 \end{align*}$$

\]

Step4: Solve for \(x\)

Subtract 4 from both sides of the equation \(9x + 4 = 22\).
\[
9x=22 - 4\\
9x = 18
\]
Divide both sides by 9.
\[
x = 2
\]

Answer:

The solution to the system of equations is \(x = 2\) and \(y=\frac{1}{2}\)