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 $y = 4$.