SOLUTION: please help I am having trouble with this problem. x + y = 4 -x +y =2

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Question 92332: please help I am having trouble with this problem.
x + y = 4
-x +y =2
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=4
-1%2Ax%2B1%2Ay=2

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=4-1%2AxSubtract 1%2Ax from both sides

y=%284-1%2Ax%29 Divide both sides by 1.


Which breaks down and reduces to



y=4-1%2Ax Now we've fully isolated y

Since y equals 4-1%2Ax we can substitute the expression 4-1%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


-1%2Ax%2B1%2Ahighlight%28%284-1%2Ax%29%29=2 Replace y with 4-1%2Ax. Since this eliminates y, we can now solve for x.

-1%2Ax%2B1%2A%284%29%2B1%28-1%29x=2 Distribute 1 to 4-1%2Ax

-1%2Ax%2B4-1%2Ax=2 Multiply



-1%2Ax%2B4-1%2Ax=2 Reduce any fractions

-1%2Ax-1%2Ax=2-4 Subtract 4 from both sides


-1%2Ax-1%2Ax=-2 Combine the terms on the right side



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


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

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



x=1 <---------------------------------One answer

Now that we know that x=1, lets substitute that in for x to solve for y

-1%281%29%2B1%2Ay=2 Plug in x=1 into the 2nd equation

-1%2B1%2Ay=2 Multiply

1%2Ay=2%2B1Add 1 to both sides

1%2Ay=3 Combine the terms on the right side

cross%28%281%2F1%29%281%29%29%2Ay=%283%2F1%29%281%2F1%29 Multiply both sides by 1%2F1. This will cancel out 1 on the left side.

y=3%2F1 Multiply the terms on the right side


y=3 Reduce


So this is the other answer


y=3<---------------------------------Other answer


So our solution is

x=1 and y=3

which can also look like

(1,3)

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

1%2Ax%2B1%2Ay=4
-1%2Ax%2B1%2Ay=2

we get


graph of 1%2Ax%2B1%2Ay=4 (red) and -1%2Ax%2B1%2Ay=2 (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 (1,3). This verifies our answer.


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Check:

Plug in (1,3) into the system of equations


Let x=1 and y=3. Now plug those values into the equation 1%2Ax%2B1%2Ay=4

1%2A%281%29%2B1%2A%283%29=4 Plug in x=1 and y=3


1%2B3=4 Multiply


4=4 Add


4=4 Reduce. Since this equation is true the solution works.


So the solution (1,3) satisfies 1%2Ax%2B1%2Ay=4



Let x=1 and y=3. Now plug those values into the equation -1%2Ax%2B1%2Ay=2

-1%2A%281%29%2B1%2A%283%29=2 Plug in x=1 and y=3


-1%2B3=2 Multiply


2=2 Add


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


So the solution (1,3) satisfies -1%2Ax%2B1%2Ay=2


Since the solution (1,3) satisfies the system of equations


1%2Ax%2B1%2Ay=4
-1%2Ax%2B1%2Ay=2


this verifies our answer.