# How to solve the system of equations 2x-y=-1 and 3x+2y=-5 by graphing?

Jul 24, 2018

From the graphs, we get point of intersection at $x = - 1$ and $y = - 1$.

#### Explanation:

The intercept of two linear graphs is the solution for $x$ and $y$.

Lets take the first equation:
$2 x - y = - 1$

Find the $x$ intercept and $y$ intercept and plot the graph.

$x$-intercept, $y = 0$
$2 x - y = - 1$

$2 x - 0 = - 1$

$2 x = - 1$

$x = - \frac{1}{2}$ ------> $x$-Intercept

$y$-intercept, $x = 0$

$2 x - y = - 1$

$2 \left(0\right) - y = - 1$

$- y = - 1$

$y = 1$------>$y$-Intercept

Lets take the second equation:
$3 x + 2 y = - 5$

Find the $x$ intercept and $y$ intercept and plot the graph.

$x$-intercept, $y = 0$
$3 x + 2 y = - 5$

$3 x + 2 \left(0\right) = - 5$

$3 x = - 5$

$x = - \frac{5}{3}$ -----> $x$-Intercept

$y$-intercept, $x = 0$
$3 x + 2 y = - 5$

$3 \left(0\right) + 2 y = - 5$

$2 y = - 5$

$y = - \frac{5}{2}$------> $y$-Intercept

**Now plot the two linear graphs and from the graph, the intersection of these tow linear graphs are the value of $x$ and $y$ satisfying both the equations. Graphs are shown below:

From the graphs, we get point of intersection at $x = - 1$ and $y = - 1$.