# How do you solve the system of linear equations y=2x-3 and y=-x+4?

Feb 19, 2016

The solution for the system of equations is:
color(blue)(x=7/3
color(blue)(y=5/3

#### Explanation:

$2 x - \textcolor{b l u e}{y} = 3$ ............equation $\left(1\right)$

$- x \textcolor{b l u e}{- y} = - 4$......equation $\left(2\right)$

Solving by elimination:

Subtracting equation $2$ from $1$:

$2 x - \cancel{\textcolor{b l u e}{y}} = 3$
$+ x \cancel{\textcolor{b l u e}{+ y}} = + 4$

$3 x = 7$

$x = \frac{7}{3}$

Finding $y$ from equation $1$

$2 x - y = 3$

$2 x - 3 = y$

$2 \times \left(\frac{7}{3}\right) - 3 = y$

$\frac{14}{3} - \frac{9}{3} = y$

$y = \frac{5}{3}$