Question

Solve the following pair of linear equations for \(x\) and \(y\) algebraically:
\(x + 2y = 9 \quad \text{and} \quad y - 2x = 2\)

Answer 1

From the first equation:

\[ x + 2y = 9 \implies x = 9 - 2y \]

Substitute this expression for \(x\) into the second equation:

\[ y - 2(9 - 2y) = 2 \]

Simplifying:

\[ y - 18 + 4y = 2 \implies 5y = 20 \implies y = 4 \]

Now substitute \(y = 4\) into \(x = 9 - 2y\):

\[ x = 9 - 2(4) = 9 - 8 = 1 \]

Thus, the solution is \(x = 1\) and \(y = 4\).