SOLUTION: Solve the following system of linear inequalities by graphing. x + 2y =3 2x – 3y = 6

Algebra ->  Linear-equations -> SOLUTION: Solve the following system of linear inequalities by graphing. x + 2y =3 2x – 3y = 6       Log On


   

Question 126101: Solve the following system of linear inequalities by graphing.
x + 2y =3
2x – 3y = 6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: these are not inequalities. These are equations.


Start with the given system of equations:

1x%2B2y=3
2x-3y=6




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

1x%2B2y=3 Start with the given equation


2y=3-x Subtract +x from both sides


2y=-x%2B3 Rearrange the equation


y=%28-x%2B3%29%2F%282%29 Divide both sides by 2


y=%28-1%2F2%29x%2B%283%29%2F%282%29 Break up the fraction


y=%28-1%2F2%29x%2B3%2F2 Reduce


Now lets graph y=%28-1%2F2%29x%2B3%2F2 (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+%28-1%2F2%29x%2B3%2F2%29+ Graph of y=%28-1%2F2%29x%2B3%2F2



So let's solve for y on the second equation

2x-3y=6 Start with the given equation


-3y=6-2x Subtract 2+x from both sides


-3y=-2x%2B6 Rearrange the equation


y=%28-2x%2B6%29%2F%28-3%29 Divide both sides by -3


y=%28-2%2F-3%29x%2B%286%29%2F%28-3%29 Break up the fraction


y=%282%2F3%29x-2 Reduce



Now lets add the graph of y=%282%2F3%29x-2 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F2%29x%2B3%2F2%2C%282%2F3%29x-2%29+ Graph of y=%28-1%2F2%29x%2B3%2F2(red) and y=%282%2F3%29x-2(green)

From the graph, we can see that the two lines intersect at the point (3,0)