How do you solve the system of equations: -3x+y=-4 and 2x-y=1?

Aug 12, 2015

Add the given equations together to get an equation in terms or just $x$; solve for $x$; then use the solution value in one of the given equations to determine $y$
$\left(x , y\right) = \left(- 5 , - 11\right)$

Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$- 3 x + y = 4$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$2 x - y = 1$

Adding [1] and [2]
[3]$\textcolor{w h i t e}{\text{XXXX}}$$- x = 5$
Multiplying by $\left(- 1\right)$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$x = - 5$

Substituting $\left(- 5\right)$ for $x$ in [1]
[5]$\textcolor{w h i t e}{\text{XXXX}}$$- 3 \left(- 5\right) + y = 4$

Simplifying
[6]$\textcolor{w h i t e}{\text{XXXX}}$$y = - 11$