# How do you solve the following system?:  x-7y=13 , 3x - 5y = 2

Dec 17, 2015

point of intersection $= \left(- \frac{51}{16} , - \frac{37}{16}\right)$

#### Explanation:

When you solve the system, you are finding the point(s) at which the two lines intersect. We can solve the system by using elimination or substitution. In this case, we will use substitution.

Equation $1$: $x - 7 y = 13$
Equation $2$: $3 x - 5 y = 2$

$1.$ Start by isolating for $x$ in equation $1$.

$x - 7 y = 13$

$x = 7 y + 13$

$2.$ Substitute $x = 7 y + 13$ into equation $2$ and isolate for $y$ to find the y-coordinate of the point of intersection.

$3 x - 5 y = 2$

$3 \left(7 y + 13\right) - 5 y = 2$

$21 y + 39 - 5 y = 2$

$16 y + 39 = 2$

$16 y = - 37$

$y = - \frac{37}{16}$

$3.$ Substitute $y = - \frac{37}{16}$ into $x = 7 y + 13$ to find the x-coordinate of the point of intersection.

$x = 7 y + 13$

$x = 7 \left(- \frac{37}{16}\right) + 13$

$x = - \frac{259}{16} + 13$

$x = - \frac{51}{16}$

$\therefore$, the point of intersection is $\left(- \frac{51}{16} , - \frac{37}{16}\right)$.