SOLUTION: Solve the system by graphing. 1. 4x+y=14 16x+4y=56 2. 6x+y=36 x+3y=23

Algebra ->  Graphs -> SOLUTION: Solve the system by graphing. 1. 4x+y=14 16x+4y=56 2. 6x+y=36 x+3y=23      Log On


   

Question 144556: Solve the system by graphing.
1. 4x+y=14
16x+4y=56
2. 6x+y=36
x+3y=23
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started


Start with the given system of equations:

4x%2By=14
16x%2B4y=56




In order to graph these equations, we need to solve for y for each equation.



So let's solve for y on the first equation

4x%2By=14 Start with the given equation


1y=14-4x Subtract 4+x from both sides


1y=-4x%2B14 Rearrange the equation


y=%28-4x%2B14%29%2F%281%29 Divide both sides by 1


y=%28-4%2F1%29x%2B%2814%29%2F%281%29 Break up the fraction


y=-4x%2B14 Reduce


Now lets graph y=-4x%2B14 (note: if you need help with graphing, check out this solver)


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-4x%2B14%29+ Graph of y=-4x%2B14



So let's solve for y on the second equation

16x%2B4y=56 Start with the given equation


4y=56-16x Subtract 16+x from both sides


4y=-16x%2B56 Rearrange the equation


y=%28-16x%2B56%29%2F%284%29 Divide both sides by 4


y=%28-16%2F4%29x%2B%2856%29%2F%284%29 Break up the fraction


y=-4x%2B14 Reduce



Now lets add the graph of y=-4x%2B14 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-4x%2B14%2C-4x%2B14%29+ Graph of y=-4x%2B14(red) and y=-4x%2B14(green)

From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.