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 \(x\).

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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 \(9x + 8y = 22\).

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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 \(y=\frac{1}{2}\)