# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent 2x+y=0 and 5x-y=7?

Mar 7, 2018

graph{(2x+y)(5x-y-7)=0 [-10, 10, -5, 5]}
color(red)(x=1 & color(magenta)(y=-2

#### Explanation:

$5 x - y = 7$
$y = 5 x - 7$

Given that, $2 x + y = 0$

Replacing, $y = 5 x - 7$ in $2 x + y = 0$

$2 x + \left(5 x - 7\right) = 0$

$7 x - 7 = 0$

$7 x = 7$

color(red)(x=1

Replacing $x = 1$, in $y = 5 x - 7$

$y = 5 \times 1 - 7$

color(magenta)(y=-2

The values are consistent.

Alternatively ,
Consider $y = 5 x - 7$ and plot the points on the graph that satisfy the equation, such as $\left(0 , - 7\right) , \left(2 , 3\right)$etc
and for $2 x + y = 0$, you could plot $\left(0 , 0\right) , \left(2 , - 2\right)$ etc

You would get two lines in the graph. Mark the point of intersection and that's the solution for the equations.
Here, the lines meet at (1,-2). Therefore the solution is, $x = 1 , y = - 2$ (which matches the answer above:) )

P.S. to get the points to plot on the graph for both the equations, replace $x$ as any value and then get the corresponding value of $y$ from the equality.

~Hope this helps!