SOLUTION: Solve the following system of linear equations, a) using Substitution In your submission, include the variable you solved for and the expression you obtained for the variable. Wr

Algebra ->  Linear-equations -> SOLUTION: Solve the following system of linear equations, a) using Substitution In your submission, include the variable you solved for and the expression you obtained for the variable. Wr      Log On


   

Question 342712: Solve the following system of linear equations,
a) using Substitution
In your submission, include the variable you solved for and the expression you obtained for the variable. Write your answer as an ordered pair.
x+2y=5
2x+y=-2
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%2B2y=5%2C2x%2By=-2%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%2By=-2 Start with the second equation


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


y=-2x-2 Rearrange the equation




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

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



x%2B2highlight%28%28-2x-2%29%29=5 Plug in y=-2x-2 into the first 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.



x%2B%282%29%28-2%29x%2B%282%29%28-2%29=5 Distribute 2 to -2x-2


x-4x-4=5 Multiply


-3x-4=5 Combine like terms on the left side


-3x=5%2B4Add 4 to both sides


-3x=9 Combine like terms on the right side


x=%289%29%2F%28-3%29 Divide both sides by -3 to isolate x



x=-3 Divide





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


So the first part of our answer is: x=-3









Since we know that x=-3 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%28-3%29-2 Plug in x=-3


y=6-2 Multiply


y=4 Combine like terms



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


So the second part of our answer is: y=4









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

So our answers are:

x=-3 and y=4

which form the point



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

Also, feel free to check out my tutoring website

Jim