SOLUTION: x + y=2 -3x +4y=36

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Question 114382This question is from textbook
: x + y=2
-3x +4y=36 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

1%2Ax%2B1%2Ay=2
-3%2Ax%2B4%2Ay=36

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.

Solve for y for the first equation

1%2Ay=2-1%2AxSubtract 1%2Ax from both sides

y=%282-1%2Ax%29 Divide both sides by 1.


Which breaks down and reduces to



y=2-1%2Ax Now we've fully isolated y

Since y equals 2-1%2Ax we can substitute the expression 2-1%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


-3%2Ax%2B4%2Ahighlight%28%282-1%2Ax%29%29=36 Replace y with 2-1%2Ax. Since this eliminates y, we can now solve for x.

-3%2Ax%2B4%2A%282%29%2B4%28-1%29x=36 Distribute 4 to 2-1%2Ax

-3%2Ax%2B8-4%2Ax=36 Multiply



-3%2Ax%2B8-4%2Ax=36 Reduce any fractions

-3%2Ax-4%2Ax=36-8 Subtract 8 from both sides


-3%2Ax-4%2Ax=28 Combine the terms on the right side



-7%2Ax=28 Now combine the terms on the left side.


cross%28%281%2F-7%29%28-7%2F1%29%29x=%2828%2F1%29%281%2F-7%29 Multiply both sides by 1%2F-7. This will cancel out -7%2F1 and isolate x

So when we multiply 28%2F1 and 1%2F-7 (and simplify) we get



x=-4 <---------------------------------One answer

Now that we know that x=-4, lets substitute that in for x to solve for y

-3%28-4%29%2B4%2Ay=36 Plug in x=-4 into the 2nd equation

12%2B4%2Ay=36 Multiply

4%2Ay=36-12Subtract 12 from both sides

4%2Ay=24 Combine the terms on the right side

cross%28%281%2F4%29%284%29%29%2Ay=%2824%2F1%29%281%2F4%29 Multiply both sides by 1%2F4. This will cancel out 4 on the left side.

y=24%2F4 Multiply the terms on the right side


y=6 Reduce


So this is the other answer


y=6<---------------------------------Other answer


So our solution is

x=-4 and y=6

which can also look like

(-4,6)

Notice if we graph the equations (if you need help with graphing, check out this solver)

1%2Ax%2B1%2Ay=2
-3%2Ax%2B4%2Ay=36

we get


graph of 1%2Ax%2B1%2Ay=2 (red) and -3%2Ax%2B4%2Ay=36 (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.


and we can see that the two equations intersect at (-4,6). This verifies our answer.


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Check:

Plug in (-4,6) into the system of equations


Let x=-4 and y=6. Now plug those values into the equation 1%2Ax%2B1%2Ay=2

1%2A%28-4%29%2B1%2A%286%29=2 Plug in x=-4 and y=6


-4%2B6=2 Multiply


2=2 Add


2=2 Reduce. Since this equation is true the solution works.


So the solution (-4,6) satisfies 1%2Ax%2B1%2Ay=2



Let x=-4 and y=6. Now plug those values into the equation -3%2Ax%2B4%2Ay=36

-3%2A%28-4%29%2B4%2A%286%29=36 Plug in x=-4 and y=6


12%2B24=36 Multiply


36=36 Add


36=36 Reduce. Since this equation is true the solution works.


So the solution (-4,6) satisfies -3%2Ax%2B4%2Ay=36


Since the solution (-4,6) satisfies the system of equations


1%2Ax%2B1%2Ay=2
-3%2Ax%2B4%2Ay=36


this verifies our answer.