SOLUTION: y=2x+1 y=3x+1 What do you do in these. Do you graph or solve it? or both

Algebra ->  Linear-equations -> SOLUTION: y=2x+1 y=3x+1 What do you do in these. Do you graph or solve it? or both      Log On


   

Question 127515: y=2x+1
y=3x+1
What do you do in these. Do you graph or solve it? or both
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system
y=2x%2B1
y=3x%2B1



3x%2B1=2x%2B1 Plug in y=3x%2B1 into the first equation. In other words, replace each y with 3x%2B1. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


3x=2x%2B1-1%29Subtract 1 from both sides


3x-2x=1-1 Subtract 2x from both sides


-x=1-1 Combine like terms on the left side


-x=0 Combine like terms on the right side


x=%280%29%2F%28-1%29 Divide both sides by -1 to isolate x



x=0 Divide




Now that we know that x=0, we can plug this into y=3x%2B1 to find y



y=3%280%29%2B1 Substitute 0 for each x


y=1 Simplify


So our answer is x=0 and y=1 which also looks like



Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.


+graph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C+2x%2B1%2C+3x%2B1%29+ Graph of y=2x%2B1 (red) and y=3x%2B1 (green)