# Where do the lines 3x+5y=78 and 2x-y=0 intersect?

Sep 13, 2017

lines intersect at $\left(6 , 12\right)$

#### Explanation:

If we equate one of the equations with the other, this will allow us to find a point or points that are common to both.

Rearrange both equations so they are in terms of y.

$y = 2 x$

$y = - \frac{3}{5} x + \frac{78}{5}$

$2 x = - \frac{3}{5} x + \frac{78}{5}$

Solving for $x$:

Multiplying both sides by $5$

$10 x = - 3 x + 78$

Adding $3 x$ to both sides:

$13 x = 78 \implies x = 6$

Plugging $6$ into the equation $y = 2 x$:

$y = 2 \left(6\right) \implies y = 12$

So lines intersect at $\left(6 , 12\right)$

Graph: