# How do you find the coordinates of the point of intersection for the pair of lines whose equations y=2x-1 and x+2y=8?

Sep 16, 2015

$x = 2 \mathmr{and} y = 3$

#### Explanation:

$y = 2 x - 1$ . . . .(1)
$x + 2 y = 8$ . . . . (2)
(1) * 2 = 2y = 4x - 2 . . . .(3)
(2) - (3) = x = 8 - 4x + 2
i.e., $4 x + x = 5 x = 8 + 2 = 10$
or $x = \frac{10}{5} = 2$
$y = 2 \cdot 2 - 1 = 3$

Sep 16, 2015

I found:
$x = 2$
$y = 3$

#### Explanation:

You can use the value of $y$ from the first equation and substitute into the second to get:
$x + 2 \left(\textcolor{red}{2 x - 1}\right) = 8$ and solve for $x$:
$x + 4 x - 2 = 8$
$5 x = 10$
$x = \frac{10}{5} = 2$
use this value back into the first equation to find $y$:
$y = 2 \cdot 2 - 1 = 4 - 1 = 3$