SOLUTION: Solve each of the following systems by graphing. 6. 4x + 3y = 12 x + y = 2

Algebra ->  Graphs -> SOLUTION: Solve each of the following systems by graphing. 6. 4x + 3y = 12 x + y = 2       Log On


   

Question 124408: Solve each of the following systems by graphing.


6.
4x + 3y = 12
x + y = 2




Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

4x%2B3y=12
1x%2By=2




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%2B3y=12 Start with the given equation


3y=12-4x Subtract 4+x from both sides


3y=-4x%2B12 Rearrange the equation


y=%28-4x%2B12%29%2F%283%29 Divide both sides by 3


y=%28-4%2F3%29x%2B%2812%29%2F%283%29 Break up the fraction


y=%28-4%2F3%29x%2B4 Reduce


Now lets graph y=%28-4%2F3%29x%2B4 (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+%28-4%2F3%29x%2B4%29+ Graph of y=%28-4%2F3%29x%2B4



So let's solve for y on the second equation

1x%2By=2 Start with the given equation


1y=2-x Subtract +x from both sides


1y=-x%2B2 Rearrange the equation


y=%28-x%2B2%29%2F%281%29 Divide both sides by 1


y=%28-1%2F1%29x%2B%282%29%2F%281%29 Break up the fraction


y=-x%2B2 Reduce



Now lets add the graph of y=-x%2B2 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-4%2F3%29x%2B4%2C-x%2B2%29+ Graph of y=%28-4%2F3%29x%2B4(red) and y=-x%2B2(green)

From the graph, we can see that the two lines intersect at the point (6,-4) (note: you might have to adjust the window to see the intersection)