# How do you find the point of intersection for x+2y=3 and 3x-y= -5?

Jul 8, 2015

You use one equation to express one of the variables in terms of the other. Then you substitute that in the other equation.

#### Explanation:

$3 x - y = - 5 \to - y = - 3 x - 5 \to y = 3 x + 5$

Then:
$x + 2 \cdot \left(3 x + 5\right) = 3 \to 7 x + 10 = 3 \to x = - 1$

From the first equation:
$y = 3 x + 5 = 3 \cdot \left(- 1\right) + 5 = 2$

So the intersection point is $\left(- 1 , 2\right)$

$- 1 + 2 \cdot 2 = 3 \mathmr{and} 3 \cdot \left(- 1\right) - 2 = - 5$