graph linear system

Question

how do I graph the linear system us  4x - y = 5 and 4x + 4y = -4?

 

will it show a reasonableness solution?

 

 

I will be using this table as well to help solve.

 

  4x - y = 5                          4x + 4y  =-4

 

   x    y                                   x       y

 

   0, -5                                   0,  -1,

   1, -1                                   1,  -2

   3,  7                                   -1,   0

Answer 1

The easy way to find out if two lines intersect is to find the slope. There are two ways to do this.

 

1) Find slope between two points on the table:

(0,-5) and (1,-1) --> 4   (0,-1) and (1,-2) --> -1

2) Solve for y

y = 4x-5 --> slope is 4   y = -1-x --> slope is -1

 

Now that we've solved for y we can solve for x.

4x-5 = -x-1

5x = 4

x = 4/5

 

Now we can find the intersection:

y = 4 * (4/5) -5 = 3 1/5 - 5 = -1 4/5

Checking our work:

y = -1 - 4/5 = -1 4/5

 

Now that you have the table you can map up the points. I would use the y intercepts (0,-5) and (0, -1) and connect them to the intersection (4/5, -5/4).