SOLUTION: 5x + y = 30 x + 6y = 4 How do I solve the above linear equations using the substitution method?

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Question 325094: 5x + y = 30
x + 6y = 4
How do I solve the above linear equations using the substitution method?
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%2By=30%2Cx%2B6y=4%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%2By=30 Start with the first equation


y=30-5x Subtract 5x from both sides


y=-5x%2B30 Rearrange the equation

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

Since y=-5x%2B30, we can now replace each y in the second equation with -5x%2B30 to solve for x



x%2B6highlight%28%28-5x%2B30%29%29=4 Plug in y=-5x%2B30 into the second equation. In other words, replace each y with -5x%2B30. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2B%286%29%28-5%29x%2B%286%29%2830%29=4 Distribute 6 to -5x%2B30


x-30x%2B180=4 Multiply


-29x%2B180=4 Combine like terms on the left side


-29x=4-180Subtract 180 from both sides


-29x=-176 Combine like terms on the right side


x=%28-176%29%2F%28-29%29 Divide both sides by -29 to isolate x


x=176%2F29 Reduce


Since we know that x=176%2F29 we can plug it into the equation y=-5x%2B30 (remember we previously solved for y in the first equation).


y=-5x%2B30 Start with the equation where y was previously isolated.


y=-5%28176%2F29%29%2B30 Plug in x=176%2F29


y=-880%2F29%2B30 Multiply


y=-10%2F29 Combine like terms


So the solutions are x=176%2F29 and y=-10%2F29


which form the ordered pair