X=-2y-3 x+2y=-5

Question

Solve system of equations by graphing

Answer 1

In order to graph these equations, we must first put them in "point-intercept" form (y=mx+b)....

      x=-2y-3.........Eq1
2y+x=-3..............subtract "2y" from both sides

    2y=-x-3...........subtract "x" from both sides

      y=(-½)x-3/2...divide both sides by 2

     m=-1/2...........slope Eq1 and...
     y-intercept is (0,-3/2), where the line crosses the y-axis

x+2y=-5..............Eq2
    2y=-x-5...........subtract "x" from both sides
      y=(-½)x-5/2...divide both sides by 2
     m=-1/2...........slope Eq2 and...
     y-intercept is (0,-5/2), where the line crosses the y-axis

We now have info for both equations to graph them
on graph paper....

Plot Eq1 y-int (0,-3/2), and from that point plot another point using
the slope (rise /run = 1/-2or -1/2)
Carefully draw a line connecting the points.

Plot Eq2 y-int (0,-5/2), and from that point plot another point using
the slope (rise /run = 1/-2 or -1/2)
Carefully draw a line connecting the points.

Examine your graph and look for the point of intersection
of the two linear equations.  We notice that these lines are

parallel and will never intersect.  Recognize that their slopes, 

m=-1/2, are the same meaning the lines are parallel.

 

Because there is no point of intersection, we conclude that there

is NO SOLUTION for this system of equations.