Answer
$r = 4$, $s = 1$
Work Step by Step
Given:
$r + 3s = 7$
$2r - s = 7$
Multiply the first equation, $r + 3s = 7$, by $2$:
$2r + 6s = 14$
Subtract the second equation, $2r - s = 7$, from the first, $2r + 6s = 14$:
$2r + 6s - (2r + -s) = 14 - (7)$
$2r - 2r + 6s - (-s) = 7$
$6s + s = 7$
$7s = 7$
Divide both sides by $7$:
$s = 1$
Substitute $s = 1$ into the first equation, $r + 3s = 7$.
$r + 3s = 7$
$r + 3(1) = 7$
$r + 3 = 7$
Subtract $3$ from both sides:
$r = 4$
$r = 4$, $s = 1$
