4x-y=8 and x+2y=2

Question

need help solvinng 4x-y=8 and x=2y=2 need to find the two points in order for me to graph.  please show how to graph it also

Answer 1

Hi Connie,

 

Let's begin by solving this system of equations algebraically and then we will show the solution graphically.

 

Algebraic Solution:

 

    1.  Our system of equations:

             Equation #1:  4x - y = 8

             Equation #2:  x + 2y = 2

    2.  Multiply each term in Equation #1 by 2:

             Equation #3:  8x - 2y = 16

    3.  Add Equation #2 to Equation #3:

             Equation #4:  9x = 18

    4.  Solve for x using Equation #4:

             9x = 18

               x = 2

    5.  Plug value for x back into Equation #2 and solve

         for y:

             x + 2y = 2

             2 + 2y = 2

                   2y = 2 - 2

                   2y = 0

                     y = 0/2

                     y = 0

 

Now let's check our answers by plugging them back into Equation #1 and see if both sides are equal:

    4x - y = 8

    4(2) - 0 = 8

    8 - 0 = 8

         8 = 8 (both sides are equal)

 

Since both sides are equal, we are confident that our answers are correct.

 

Now we'll show the graphical solution giving the same solution as our algebraic solution above.  First, we'll transform each equation from standard form into slope-intercept form, so it will be easy to plug in values for x and get our values for y:

    1.  Equation #1:

             4x - y = 8 (standard form)

             -y = -4x + 8

             (-1)(-y) = (-1)(-4x) + (-1)(8)

             y = 4x - 8 (slope-intercept form)

    2.  Equation #2:                              

             x + 2y = 2 (standard form)

             2y = -x + 2

             y = -x/2 + 2/2

             y = -0.5x + 1(slope intercept form)

 

Below is the link to our graphs of the two equations (in slope-intercept form) where the blue graph is for Equation #1, the red graph is for Equation #2, and the coordinates of the intersection point (the pink cross:  x=2 and y=0) is our graphical solution (same as our algebraic solution above):

 

https://dl.dropbox.com/s/9bclzxn9uaohs6l/Graphical_Solution.png?raw=1

 

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan. 

Answer 2

For 4x - y = 8: (0, -8), (2, 0)

For x + 2y = 2: (0, 1), (2, 0)

 

Substituting 0  (zero) for x and then y is usually an easy way to get two points.