How do you solve the system x+2y=5 and 5x-y=3?

Jun 4, 2015

From the first equation we learn that
$x = 5 - 2 y$

If we substitute that value for $x$ in the second equation:
$5 \cdot \left(5 - 2 y\right) - y = 3 \to$
$25 - 10 y - y = 3 \to$ subtract 3
$22 - 11 y = 0 \to 22 = 11 y \to y = 2$
Back to the first equation:
$x = 5 - 2 \cdot 2 = 1$

$1 + 2 \cdot 2 = 5 \mathmr{and} 5 \cdot 1 - 2 = 3$