Question

Help!! I am having difficulty with a problem for hours now and if I could get some help, my head might stop pounding.Solve each system graphically. if a system has an infinite number of solutions, use set builder notation to write the solution set. If a system has no solution, state this. 2x - y = 4, 5x - y =13

Answer 1

Draw a Cartesian coordinate system.

Now :

2 x - y = 4


for x = 0

2 x - y = 4

2 * 0 - y = 4

- y = 4 Multiply both sides by - 1

y = - 4

This is first point ( x = 0 , y = 4 )


for y = 0

2 x - y = 4

2 x - 0 = 4

2 x = 4 Divide both sides by 2

x = 2

This is second point ( x = 2 , y = 0 )


Draw straight line between this two point.



5 x - y = 13


for x = 0

5 x - y = 13

5 * 0 - y = 13

- y = 13 Multiply both sides by - 1

y = - 13

This is first point ( x = 0 , y = - 13 )


for y = 0

5 x - y = 13

5 x - 0 = 13

5 x = 13 Divide both sides by 5

x = 13 / 5 = 2.6

This is second point ( x = 2.6 , y = 0 )


Draw straight line between this two point.


Intersection point of this two lines is the solution.

Coordinate of solution:

x = 3 , y = 2

You can write the solution like :

( 3 , 2 )


If you want to see graph in google type :

function graphs online

When you see list of results click on :

Draw Function Graphs - Plotter - Rechneronline


When page be open in blue rectangle type :

2 x - 4

In gray rectangle type :

5 x - 13


Set:

Range y-axis from - 15 to 5

and click option :

Draw

You will see graphs


Remark:

2 x - y = 4

is same

y = 2 x - 4


5 x - y = 13

is same

y = 5 x - 13