Question

Solve the system by graphing:2x – y= -14x - 2y = 6Solution(s):

Answer 1

To find the solution of the system by graphing we need to plot each line in the plane and look for the intersection.

First we need to write both equations in terms of y:

`\begin{gathered} y=2x+1 \\ y=2x-3 \end{gathered}`

now we need to find two points for each of this lines. To do this we give values to the variable x and find y.

For the equation 2x-y=-1, if x=0 then:

`y=1`

so we have the point (0,1).

If x=1, then:

`y=3`

so we have the point (1,3).

Now we plot this points on the plane and join them with a straight line.

Now we look for two points of the second equation.

If x=0, then:

`y=-3`

so we have the point (0,-3)

If x=1, then:

`y=-1`

so we have the point (1,-1).

We plot the points and join them wiith a line, then we have:

once we have both lines in the plane we look for the intersection. In this case we notice that the lines are parallel; this means that they wont intersect.

Therefore the system of equations has no solutions.