SOLUTION: How do you use substitution to solve each system of equations. {12x+y=21 {18x-3y=-36

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: How do you use substitution to solve each system of equations. {12x+y=21 {18x-3y=-36      Log On


   

Question 165385This question is from textbook Algebra 2
: How do you use substitution to solve each system of equations.
{12x+y=21
{18x-3y=-36 This question is from textbook Algebra 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%2812x%2By=21%2C18x-3y=-36%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

12x%2By=21 Start with the first equation


y=21-12x Subtract 12x from both sides


y=-12x%2B21 Rearrange the equation


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

Since y=-12x%2B21, we can now replace each y in the second equation with -12x%2B21 to solve for x



18x-3highlight%28%28-12x%2B21%29%29=-36 Plug in y=-12x%2B21 into the second equation. In other words, replace each y with -12x%2B21. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



18x%2B%28-3%29%28-12%29x%2B%28-3%29%2821%29=-36 Distribute -3 to -12x%2B21


18x%2B36x-63=-36 Multiply


54x-63=-36 Combine like terms on the left side


54x=-36%2B63Add 63 to both sides


54x=27 Combine like terms on the right side


x=%2827%29%2F%2854%29 Divide both sides by 54 to isolate x



x=1%2F2 Reduce





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


So the first part of our answer is: x=1%2F2









Since we know that x=1%2F2 we can plug it into the equation y=-12x%2B21 (remember we previously solved for y in the first equation).



y=-12x%2B21 Start with the equation where y was previously isolated.


y=-12%281%2F2%29%2B21 Plug in x=1%2F2


y=-12%2F2%2B21 Multiply


y=15 Combine like terms and reduce. (note: if you need help with fractions, check out this solver)



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


So the second part of our answer is: y=15









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

So our answers are:

x=1%2F2 and y=15

which form the ordered pair