SOLUTION: Solve the following system of equations. (this means – find the value for X and the value for Y - they should be the SAME for each equation!)You may use the elimination or substit

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: Solve the following system of equations. (this means – find the value for X and the value for Y - they should be the SAME for each equation!)You may use the elimination or substit      Log On


   

Question 360764: Solve the following system of equations. (this means – find the value for X and the value for Y - they should be the SAME for each equation!)You may use the elimination or substitution method:
x – y = 1
2x – y = 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%28x-y=1%2C2x-y=5%29


-1%282x-y%29=-1%285%29 Multiply the both sides of the second equation by -1.


-2x%2By=-5 Distribute and multiply.


So we have the new system of equations:
system%28x-y=1%2C-2x%2By=-5%29


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


%28x-y%29%2B%28-2x%2By%29=%281%29%2B%28-5%29


%28x-2x%29%2B%28-y%2By%29=1-5 Group like terms.


-x%2B0y=-4 Combine like terms.


-x=-4 Simplify.


x=%28-4%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=4 Reduce.


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x-y=1 Now go back to the first equation.


4-y=1 Plug in x=4.


-y=1-4 Subtract 4 from both sides.


-y=-3 Combine like terms on the right side.


y=%28-3%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=3 Reduce.


So the solutions are x=4 and y=3.


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 x-y=1 (red) and 2x-y=5 (green)


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim