SOLUTION: x-y=-1 2x-3y=-5

Algebra.Com
Question 175938: x-y=-1
2x-3y=-5

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

Start with the given system of equations:



Multiply the both sides of the first equation by -3.


Distribute and multiply.


So we have the new system of equations:



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:





Group like terms.


Combine like terms.


Simplify.


Divide both sides by to isolate .


Reduce.


------------------------------------------------------------------


Now go back to the first equation.


Plug in .


Multiply.


Add to both sides.


Combine like terms on the right side.


Divide both sides by to isolate .


Reduce.


So our answer is and .


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of (red) and (green)

RELATED QUESTIONS

x+y=1... (answered by rapaljer)
x=y-1 2x=3y (answered by Taino)
(2x-1)+(3y+2)i=5-4I,then (X,... (answered by josgarithmetic)
2x-3y=-1... (answered by drk)
2x-3y=-1 y= x... (answered by mananth)
2x-3y=-1... (answered by Boreal)
6x+3y=5... (answered by scott8148)
y=2x-1... (answered by Fombitz)