Construct a system of two linear equations where (-2, 3) is a solution to the first equation but not to the second equation, and where (5, -2)

Question

You need to write the equations of your system and graph them on the same graph.

Explain how your graph shows that your system satisfies the 2 required conditions.

Answer 1

Hello Lory

I think you are missing part of the problem... But let me help you out with at least the first part of the problem.  So, you want the answer of the first equation to be (-2, 3).  

 

You can choose any expression using x and y that you want.

 

examples 7x-4y, 3x+y, -2x-4y, any thing at all

 

Lets us choose 7x-4y

Next, and this is the important part, plug in into the expression 7x-4y, -2 for x and 3 for y. 

 

So,

7x- 4y

7(-2)+ 4(3)

-14 + 12

  -2

Then, all you have to rewrite the expression 7x-4y as an equation 

7x-4y= -2.  This becomes the first equation.  For the second equation make it up again.  Let's use:

 

5x-2y= 3       I made all the numbers up.  (-2,3) should not satisfy 

                     this equation. 

 

5x - 2y = 3

5(-3) - 2(3) = 3   Plugging the values for x and y, -2 and 3, respectively 

-15-6           = 3

 -21.          = 3

So, (-2,3) only satisfy the first equation and not the second.

 

Now, we proceed to graph them:

1) 7x-4y =-2             I am going to rewrite this equation in the slope-

                                Intercept form, y= mx+b.

    7x-4y. = -2

     -7x           -7x       Subtract 7x from both sides

        -4y  = -7x -2      Divide both sides by -4

  y=    (7/4)x + 1/2

 

So, the first equation has a slope of 7/4 and a y-intercept of 1/2.  To graph this, go to 1/2 on the y intercept and plug that point.  From 1/2 on the y axis go up 7 units up and 4 to the right And plug that point.  Now, draw the line. 

 

Next, I am going to rewrite the second equation, 5x-2y=3, in the slope intercept form so, we can graph it.

 

5x - 2y = 3

-5x            -5x

        -2 y = -5x+ 3

               y= (5/2)x + 3/2

To graph this equation, start at 3//, 1.5, on the y axis. Plug a point there.  From that point, move up 5 units and the 2 units to the right.  Now create a line by connecting both points.  Don't forget to extent the line beyond these to points, after all it is a line.

 

Now, to show that the graphs satisfy the two given conditions.  Look at line #1. It should pass by (-2,3).  However, our second line should not pass through (-2,3).

 

I hope this helps out.  

D.Y. T.

dont forget to rate me :)

 

P.s, try to fix the question. It has missing information