SOLUTION: The directions on my paper say to solve each system By graphing. Show your graphs and solutions. I am confused On how to solve and graph the problem y=3x+2 and y=2x+1(both on sa

Algebra ->  Systems-of-equations -> SOLUTION: The directions on my paper say to solve each system By graphing. Show your graphs and solutions. I am confused On how to solve and graph the problem y=3x+2 and y=2x+1(both on sa      Log On


   

Question 919136: The directions on my paper say to solve each system
By graphing. Show your graphs and solutions. I am confused
On how to solve and graph the problem y=3x+2 and y=2x+1(both on same question)
Please help?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A system of linear equations means two or more linear equations.
-you have two linear equations
y=3x%2B2...eq.1
y=2x%2B1........eq.2
___________________
If these two linear equations intersect, that point of intersection is called the solution to the system of linear equations.The solution is where the equations 'meet' or intersect.
first, I will write your equations in a standard form:

-3x%2By=2...eq.1
-2x%2By=1........eq.2
___________________
now, solve system by graphing
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-3x%2By=2

-2x%2By=1





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


-3x%2By=2 Start with the given equation



1y=2%2B3x Add 3+x to both sides



1y=%2B3x%2B2 Rearrange the equation



y=%28%2B3x%2B2%29%2F%281%29 Divide both sides by 1



y=%28%2B3%2F1%29x%2B%282%29%2F%281%29 Break up the fraction



y=3x%2B2 Reduce



Now lets graph y=3x%2B2 (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+3x%2B2%29+ Graph of y=3x%2B2




So let's solve for y on the second equation


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



1y=1%2B2x Add 2+x to both sides



1y=%2B2x%2B1 Rearrange the equation



y=%28%2B2x%2B1%29%2F%281%29 Divide both sides by 1



y=%28%2B2%2F1%29x%2B%281%29%2F%281%29 Break up the fraction



y=2x%2B1 Reduce





Now lets add the graph of y=2x%2B1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2B2%2C2x%2B1%29+ Graph of y=3x%2B2(red) and y=2x%2B1(green)


From the graph, we can see that the two lines intersect at the point (-1,-1) (note: you might have to adjust the window to see the intersection)