# How do you solve 4x - 3y = 17, 5x + 4y = 60?

Nov 13, 2015

$x = 8$, $y = 5$.

#### Explanation:

From the first equation, you know that

$x = \frac{17 + 3 y}{4}$

Substitute this value in the second equation:

$5 \left(\frac{17 + 3 y}{4}\right) + 4 y = 60 \to \frac{85 + 15 y}{4} + 4 y = 60$

We can multiply everything by $4$ to get rid of the denominator:

$85 + 15 y + 16 y = 240$

Isolating the $y$ terms:

$31 y = 155 \to y = \frac{155}{31} = 5$

Now that we knoe that $y = 5$, we can obtain $x$ by substitution:

$4 x - 3 y = 17 \to 4 x - 15 = 17 \to 4 x = 32$

and thus $x = 8$