Answer
The solution to this system of equations is $(300, 150)$.
Work Step by Step
It looks like using the elimination method is an easier way to solve this equation.
We don't like to work with fractions, so we want to convert the first equation to one that does not contain any fractions. We do this by multiplying the equation by the least common denominator for all the terms, which is $3$:
$3(\frac{x}{3} + \frac{4y}{3}) = 3(300)$
$x + 4y = 900$
Thus, the given system is equivalent to
$ x + 4y = 900$
$3x - 4y = 300$
Both equations now have the opposite numerical coefficients for $y$ so we can eliminate the $y$ terms by adding the equations together:
$(x+4y)+(3x-4y) = 900+300$
$4x=1200$
Divide each side by $4$ to solve for $x$:
$x = 300$
Now that we have the value for $x$, we can plug it into one of the equations to solve for $y$.
Let us plug in the value for $x$ into the second equation:
$3(300) - 4y = 300$
$900 - 4y = 300$
Subtract $900$ from both sides of the equation to isolate constants to the right side of the equation:
$-4y = -600$
Divide both sides by $-4$ to solve for $y$:
$y = 150$
The solution to this system of equations is $(300, 150)$.
