Expert: Bobby Soltani - 12/28/2004

Question
Solve the system by graphing
2x+y=1
x=2y+8

The formula that is supposed to be used is
mx+b=y but, I don't know how to apply that to the above. Can you help me?

Answer
Hi Diane,

To get the equations into the form above, you must solve each one for y.  Here's how:

2x+y=1
subtract 2x from both sides
y = -2x+1

Second equation
x = 2y+8
subtract 8 from both sides
x-8 = 2y
divide both sides by 2
(1/2)x - 4 = y
or
y = (1/2)x - 4

When you have the equations in the form y = mx + b, you can use this to graph it.  m is the slope (that is, the rise over the run), and b is the y intercept.

For equation 1, m = -2/1, and b = 1.  So, draw one point on the y axis (vertical axis) at y = 1.  Then the rise is -2 so go down 2 and and run is 1 so go to the right 1 and draw another point.  Now connect these two points and extend the line in both directions in a straight line.

For the second equation, b = -4, and m = 1/2.  So, the first point is at y = -4 on the y-axis.  Then, go up 1 and to the right 2 and draw the second point.  Extend this line like the first.

Whereever these line intersect is the solution to the equation.  For example, if the lines intersect at (4,3), then the solution is x=4 and y = 3.

Let me know if you have any questions.

Bobby