How do I use a graph to solve the solution of the system of equations y=−2x+4 and y=−2x−3?

1 Answer
seph
Oct 25, 2014

Graph your equations and check where they intersect.
If they do intersect, you have a solution.

If not, the system of equations do not have a solution. For linear equations, this happens when the lines are parallel (i.e. they have the same slope)

For your system of equations

y=−2x+4
y=−2x−3

One look and we know that your equations have the same slope.
Your system of equations do not have a solution.

But if your graph is not accurate enough, it will be hard to know the actual answer.

Let's try to answer your system of equations algebraically.

y=−2x+4
y=−2x−3

Isolate one variable in one of the equations and substitute its equivalent to the other equation.

For your system of equations, y is already is already isolated.
Let's substitute the first into the next equation

y=−2x+4
y=−2x−3

⇒−2x+4=−2x−3
⇒−2x+4+2x=−3
⇒4=−3

Since 4≠3, your system of equations do not have a solution

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