SOLUTION: solve the linear equation by substitution x-3y=5 -2x+6y=-10

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Question 134454: solve the linear equation by substitution
x-3y=5
-2x+6y=-10
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:

system%28x-3y=5%2C-2x%2B6y=-10%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

x-3y=5 Start with the first equation


-3y=5-x Subtract x from both sides


-3y=-x%2B5 Rearrange the equation


y=%28-x%2B5%29%2F%28-3%29 Divide both sides by -3


y=%28%28-1%29%2F%28-3%29%29x%2B%285%29%2F%28-3%29 Break up the fraction


y=%281%2F3%29x-5%2F3 Reduce



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

Since y=%281%2F3%29x-5%2F3, we can now replace each y in the second equation with %281%2F3%29x-5%2F3 to solve for x



-2x%2B6highlight%28%28%281%2F3%29x-5%2F3%29%29=-10 Plug in y=%281%2F3%29x-5%2F3 into the first equation. In other words, replace each y with %281%2F3%29x-5%2F3. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



-2x%2B%286%29%281%2F3%29x%2B%286%29%28-5%2F3%29=-10 Distribute 6 to %281%2F3%29x-5%2F3


-2x%2B%286%2F3%29x-30%2F3=-10 Multiply


-2x%2B2x-10=-10 Reduce


-30=-30 Combine like terms on the left side


0=-30%2B30Add 30 to both sides


0=0 Combine like terms on the right side



Since this equation is always true for any x value, this means x can equal any number. So there are an infinite number of solutions.