Solve system of equations by showing the graphing method.

Question

Solve the system of equations by showing the graphing method.

5x+4y=40

5x+2y=30

Answer 1

This is a description of what the graph should look like:

 

Solve both equations for y in the slope-intercept form:

 

1. 5x+4y=40

 

4y=-5x+40

 

y=-(5/4)x+10, >>>>>the slope of this equation, m₁=-5/4, and the y₁-intercept is 10

 

2.  5x+2y=30

 

2y=-5x+30

 

y=-(5/2)x+15,  >>>>>the slope of this equation, m₂=-5/2, and the y₂-intercept is 15

 

 

 

The lines should intersect at:

 

-(5/2)x+15=-(5/4)x+10, setting the two equations equal to each other.

 

(-5x+30)/2=(-5x+40)/4

 

4(-5x+30)=2*(-5x+40)

 

2(-5x+30)=-5x+40

 

-10x+60=-5x+40

 

20=5x

 

4=x

 

and since

 

5x+2y=30

 

5(4)+2y=30

 

2y=30-20

 

y=10

 

Giving a point of intersection at (4,10)

 

 

 

Answer 2

Draw the two lines representing the two equations on the same coordinate system.

 

For the first equation, plot the points (0, 10) and (8, 0).  Connect these two points in the straight line.  Call this L1.

For the second equation, plot the points (0, 15) and (6, 0).  Connect these two points in a straight line.  Call this L2.

 

Then find the point of intersection between L1 and L2.  That point of intersection is your solution.