Answer
$x=300; y=200$
Work Step by Step
Let $x$ and $y$ be the number of gallons of 87-octane gasoline and of 92-octane gasoline, respectively.
$x+y=500 \\ 0.87 x+0.92 y=(0.89)(500)$
Therefore, the system of two equations is:
$x+y=500 \\ 0.87 x+0.92 y=445$
Multiply the first equation by $-0.92$ and then add the new equation to equation $2$.
$-0.92x-0.92y+0.87x+0.92 y=-460+445 $
The yields $x=300$
Substitute the value of $x$ into the first equation to get the value of $y$.
$300+y=500 \implies y=200 $
Thus, $x=300; y=200$
