Question

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`?

Answer 1

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

Explanation:

`5x-y=7`
`y=5x-7`

Given that, `2x+y=0`

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

`2x+(5x-7)=0`

`7x-7=0`

`7x=7`

`color(red)(x=1`

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

`y=5xx1-7`

`color(magenta)(y=-2`

The values are consistent.

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