SOLUTION: Ive been working on a review for a test next tuesday, but i keep getting confused with this type of equation by using substitution. {2x-y=2 {3x-2y=11

Algebra ->  Systems-of-equations -> SOLUTION: Ive been working on a review for a test next tuesday, but i keep getting confused with this type of equation by using substitution. {2x-y=2 {3x-2y=11      Log On


   

Question 499795: Ive been working on a review for a test next tuesday, but i keep getting confused with this type of equation by using substitution.
{2x-y=2
{3x-2y=11
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%282x-y=2%2C3x-2y=11%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

2x-y=2 Start with the first equation


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


-y=-2x%2B2 Rearrange the equation


y=%28-2x%2B2%29%2F%28-1%29 Divide both sides by -1


y=%28%28-2%29%2F%28-1%29%29x%2B%282%29%2F%28-1%29 Break up the fraction


y=2x-2 Reduce



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

Since y=2x-2, we can now replace each y in the second equation with 2x-2 to solve for x



3x-2highlight%28%282x-2%29%29=11 Plug in y=2x-2 into the second equation. In other words, replace each y with 2x-2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



3x%2B%28-2%29%282%29x%2B%28-2%29%28-2%29=11 Distribute -2 to 2x-2


3x-4x%2B4=11 Multiply


-x%2B4=11 Combine like terms on the left side


-x=11-4Subtract 4 from both sides


-x=7 Combine like terms on the right side


x=%287%29%2F%28-1%29 Divide both sides by -1 to isolate x



x=-7 Divide





-----------------First Answer------------------------------


So the first part of our answer is: x=-7









Since we know that x=-7 we can plug it into the equation y=2x-2 (remember we previously solved for y in the first equation).



y=2x-2 Start with the equation where y was previously isolated.


y=2%28-7%29-2 Plug in x=-7


y=-14-2 Multiply


y=-16 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: y=-16









-----------------Summary------------------------------

So our answers are:

x=-7 and y=-16

which form the point