# What is the intersection point for y = 3x - 4 and 2x - y = 1?

Mar 28, 2015

$y = 3 x - 4$
$2 x - y = 1$

The first equation gives us an immediate expression for $y$ which we can substitute into the second equation:
$2 x - \left(3 x - 4\right) = 1$
$\rightarrow - x + 4 = 1$
$\rightarrow x = 3$

Substituting $x = 3$ back into the first equation:
$y = 3 \left(3\right) - 4$
$\rightarrow y = 5$

The given lines intersect (have a common solution at)
$\left(x , y\right) = \left(3 , 5\right)$