Question 961590
Hello!
Let's see if I can help you.
We can solve this system with substitution.
First pay attention to the first equation.
{{{4y=3x-13}}}
Let's arrange it so it looks like "y = ...", so we can plug that value instead of "y" in the second equation. So basically divide 4 from both sides to isolate y.
{{{y=(3/4)x-13/4}}}
We can turn those fractions into decimals to make it a bit easier to work with. It depends if you work better with fractions or decimals.
{{{y=0.75x-3.25}}}
Now, plug ({{{0.75x-3.25}}}) instead of y in the second equation:
{{{6x+5(0.75x-3.25)=52}}}
So now we are trying to solve for x.
{{{6x+3.75x-16.25=52}}}
{{{9.75x-16.25=52}}}
{{{9.75x=68.25}}}
{{{x=7}}}
So we have x now. But wait, we still haven't found y yet. Simply put 7 instead of x in either of the two equations and solve for y. (We'll use the second equation)
{{{6(7)+5y=52}}}
{{{42+5y=52}}}
{{{5y=10}}}
{{{y=2}}}


So there you have it! We now know that x = 7 and y = 2.
Hope I helped.