Answer
$x = 5$, $y = 4$, or $(5,4)$
Work Step by Step
Given:
$20x + 5y = 120$
$10x + 7.5y = 80$
Multiply both sides of the second equation by $2$:
$20x + 15x = 160$
Subtract the first equation, $20x + 5y = 120$, from the second, $20x + 15x = 160$.
$20x + 15y - (20x + 5y) = 160 - (120)
\\20x - 20x + 15y - 5y = 160 - 120
\\10y = 40$
Divide both sides by $10$:
$y = 4$
Substitute $y = 4$ into the first equation, $20x + 5y = 120$:
$20x+5y=120
\\20x + 5(4) = 120
\\20x + 20 = 120$
Subtract $20$ from both sides:
$20x = 100$
Divide both sides by $20$:
$x = 5$
Thus, $x = 5$ and $y = 4$
