SOLUTION: Solve the system of linear equations by the substitution method. 5x + 4 y = 14 15x – 2y = 7 This is what I have so far...but I get lost somehow ..maybe I just don't undesta

Algebra ->  Expressions-with-variables -> SOLUTION: Solve the system of linear equations by the substitution method. 5x + 4 y = 14 15x – 2y = 7 This is what I have so far...but I get lost somehow ..maybe I just don't undesta      Log On


   

Question 150797: Solve the system of linear equations by the substitution method.
5x + 4 y = 14
15x – 2y = 7

This is what I have so far...but I get lost somehow ..maybe I just don't undestand the substitution method thoroughly
5x +4y = 14
-4y -4y
5x = 14 – 4y divide each by 5
5 5 5
x = 14 – 4y
5 5
5(14 – 4y) + 4y = 14
5 5
39 - 29y + 4y = 14
5 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%285x%2B4y=14%2C15x-2y=7%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

5x%2B4y=14 Start with the first equation


4y=14-5x Subtract 5x from both sides


4y=-5x%2B14 Rearrange the equation


y=%28-5x%2B14%29%2F%284%29 Divide both sides by 4


y=%28%28-5%29%2F%284%29%29x%2B%2814%29%2F%284%29 Break up the fraction


y=%28-5%2F4%29x%2B7%2F2 Reduce



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

Since y=%28-5%2F4%29x%2B7%2F2, we can now replace each y in the second equation with %28-5%2F4%29x%2B7%2F2 to solve for x



15x-2highlight%28%28%28-5%2F4%29x%2B7%2F2%29%29=7 Plug in y=%28-5%2F4%29x%2B7%2F2 into the first equation. In other words, replace each y with %28-5%2F4%29x%2B7%2F2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



15x%2B%28-2%29%28-5%2F4%29x%2B%28-2%29%287%2F2%29=7 Distribute -2 to %28-5%2F4%29x%2B7%2F2


15x%2B%2810%2F4%29x-14%2F2=7 Multiply


%284%29%2815x%2B%2810%2F4%29x-14%2F2%29=%284%29%287%29 Multiply both sides by the LCM of 4. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



60x%2B10x-28=28 Distribute and multiply the LCM to each side



70x-28=28 Combine like terms on the left side


70x=28%2B28Add 28 to both sides


70x=56 Combine like terms on the right side


x=%2856%29%2F%2870%29 Divide both sides by 70 to isolate x



x=4%2F5 Reduce





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


So the first part of our answer is: x=4%2F5









Since we know that x=4%2F5 we can plug it into the equation y=%28-5%2F4%29x%2B7%2F2 (remember we previously solved for y in the first equation).



y=%28-5%2F4%29x%2B7%2F2 Start with the equation where y was previously isolated.


y=%28-5%2F4%29%284%2F5%29%2B7%2F2 Plug in x=4%2F5


y=-20%2F20%2B7%2F2 Multiply


y=5%2F2 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=5%2F2









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

So our answers are:

x=4%2F5 and y=5%2F2

which forms the ordered pair