SOLUTION: Solve the system of equations using the substitution method. If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no s

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Question 133146: Solve the system of equations using the substitution method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-3x + y = 1
5x + 2y = -4

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%28-3x%2By=1%2C5x%2B2y=-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

-3x%2By=1 Start with the first equation


y=1%2B3x Add 3x to both sides


y=%2B3x%2B1 Rearrange the equation


y=%28%2B3x%2B1%29%2F%281%29 Divide both sides by 1


y=%28%28%2B3%29%2F%281%29%29x%2B%281%29%2F%281%29 Break up the fraction


y=3x%2B1 Reduce



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

Since y=3x%2B1, we can now replace each y in the second equation with 3x%2B1 to solve for x



5x%2B2highlight%28%283x%2B1%29%29=-4 Plug in y=3x%2B1 into the first equation. In other words, replace each y with 3x%2B1. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



5x%2B%282%29%283%29x%2B%282%29%281%29=-4 Distribute 2 to 3x%2B1


5x%2B6x%2B2=-4 Multiply


11x%2B2=-4 Combine like terms on the left side


11x=-4-2Subtract 2 from both sides


11x=-6 Combine like terms on the right side


x=%28-6%29%2F%2811%29 Divide both sides by 11 to isolate x



x=-6%2F11 Reduce





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


So the first part of our answer is: x=-6%2F11









Since we know that x=-6%2F11 we can plug it into the equation y=3x%2B1 (remember we previously solved for y in the first equation).



y=3x%2B1 Start with the equation where y was previously isolated.


y=3%28-6%2F11%29%2B1 Plug in x=-6%2F11


y=-18%2F11%2B1 Multiply


y=-7%2F11 Combine like terms (note: if you need help with fractions, check out this solver)



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


So the second part of our answer is: y=-7%2F11









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

So our answers are:

x=-6%2F11 and y=-7%2F11

which form the point