SOLUTION: what is the answer to 2x-3y=-1 y=x-1

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Question 680980: what is the answer to 2x-3y=-1 y=x-1
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

you have a system of linear functions and solution will be coordinates (x,y) of their intersection point

2x-3y=-1
y=x-1.....=>......-x%2By=-1

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


2x-3y=-1

-x%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


2x-3y=-1 Start with the given equation



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



-3y=-2x-1 Rearrange the equation



y=%28-2x-1%29%2F%28-3%29 Divide both sides by -3



y=%28-2%2F-3%29x%2B%28-1%29%2F%28-3%29 Break up the fraction



y=%282%2F3%29x%2B1%2F3 Reduce



Now lets graph y=%282%2F3%29x%2B1%2F3 (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+%282%2F3%29x%2B1%2F3%29+ Graph of y=%282%2F3%29x%2B1%2F3




So let's solve for y on the second equation


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



1y=-1%2Bx Add +x to both sides



1y=%2Bx-1 Rearrange the equation



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



y=%28%2B1%2F1%29x%2B%28-1%29%2F%281%29 Break up the fraction



y=x-1 Reduce





Now lets add the graph of y=x-1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%282%2F3%29x%2B1%2F3%2Cx-1%29+ Graph of y=%282%2F3%29x%2B1%2F3(red) and y=x-1(green)


From the graph, we can see that the two lines intersect at the point (4,3) (note: you might have to adjust the window to see the intersection)