SOLUTION: x=2y-3 x=2y+4 solve for each system of equation

Algebra ->  Expressions-with-variables -> SOLUTION: x=2y-3 x=2y+4 solve for each system of equation       Log On


   

Question 702174: x=2y-3 x=2y+4 solve for each system of equation
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x=2y-3
x=2y%2B4
_____________
x-2y=-3
x-2y=4
_______________

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



Start with the given system of equations:


1x-2y=-3

1x-2y=4





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-2y=-3 Start with the given equation



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



-2y=-x-3 Rearrange the equation



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



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



y=%281%2F2%29x%2B3%2F2 Reduce



Now lets graph y=%281%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+%281%2F2%29x%2B3%2F2%29+ Graph of y=%281%2F2%29x%2B3%2F2




So let's solve for y on the second equation


1x-2y=4 Start with the given equation



-2y=4-x Subtract +x from both sides



-2y=-x%2B4 Rearrange the equation



y=%28-x%2B4%29%2F%28-2%29 Divide both sides by -2



y=%28-1%2F-2%29x%2B%284%29%2F%28-2%29 Break up the fraction



y=%281%2F2%29x-2 Reduce





Now lets add the graph of y=%281%2F2%29x-2 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x%2B3%2F2%2C%281%2F2%29x-2%29+ Graph of y=%281%2F2%29x%2B3%2F2(red) and y=%281%2F2%29x-2(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.