SOLUTION: please can you help with this problem -3x+2y=8 3x+2y=8 university of phoenix elementary and intermidiate algebra

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Question 91747: please can you help with this problem -3x+2y=8 3x+2y=8 university of phoenix elementary and intermidiate algebra
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Lets solve this system using substitution


Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

-3%2Ax%2B2%2Ay=8
3%2Ax%2B2%2Ay=8

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

2%2Ay=8%2B3%2AxAdd 3%2Ax to both sides

y=%288%2B3%2Ax%29%2F2 Divide both sides by 2.


Which breaks down and reduces to



y=4%2B%283%2F2%29%2Ax Now we've fully isolated y

Since y equals 4%2B%283%2F2%29%2Ax we can substitute the expression 4%2B%283%2F2%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


3%2Ax%2B2%2Ahighlight%28%284%2B%283%2F2%29%2Ax%29%29=8 Replace y with 4%2B%283%2F2%29%2Ax. Since this eliminates y, we can now solve for x.

3%2Ax%2B2%2A%284%29%2B2%283%2F2%29x=8 Distribute 2 to 4%2B%283%2F2%29%2Ax

3%2Ax%2B8%2B%286%2F2%29%2Ax=8 Multiply



3%2Ax%2B8%2B3%2Ax=8 Reduce any fractions

3%2Ax%2B3%2Ax=8-8 Subtract 8 from both sides


3%2Ax%2B3%2Ax=0 Combine the terms on the right side



6%2Ax=0 Now combine the terms on the left side.


cross%28%281%2F6%29%286%2F1%29%29x=%280%2F1%29%281%2F6%29 Multiply both sides by 1%2F6. This will cancel out 6%2F1 and isolate x

So when we multiply 0%2F1 and 1%2F6 (and simplify) we get



x=0 <---------------------------------One answer

Now that we know that x=0, lets substitute that in for x to solve for y

3%280%29%2B2%2Ay=8 Plug in x=0 into the 2nd equation

0%2B2%2Ay=8 Multiply

2%2Ay=8%2B0Add 0 to both sides

2%2Ay=8 Combine the terms on the right side

cross%28%281%2F2%29%282%29%29%2Ay=%288%2F1%29%281%2F2%29 Multiply both sides by 1%2F2. This will cancel out 2 on the left side.

y=8%2F2 Multiply the terms on the right side


y=4 Reduce


So this is the other answer


y=4<---------------------------------Other answer


So our solution is

x=0 and y=4

which can also look like

(0,4)

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

-3%2Ax%2B2%2Ay=8
3%2Ax%2B2%2Ay=8

we get


graph of -3%2Ax%2B2%2Ay=8 (red) and 3%2Ax%2B2%2Ay=8 (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 (0,4). This verifies our answer.


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Check:

Plug in (0,4) into the system of equations


Let x=0 and y=4. Now plug those values into the equation -3%2Ax%2B2%2Ay=8

-3%2A%280%29%2B2%2A%284%29=8 Plug in x=0 and y=4


0%2B8=8 Multiply


8=8 Add


8=8 Reduce. Since this equation is true the solution works.


So the solution (0,4) satisfies -3%2Ax%2B2%2Ay=8



Let x=0 and y=4. Now plug those values into the equation 3%2Ax%2B2%2Ay=8

3%2A%280%29%2B2%2A%284%29=8 Plug in x=0 and y=4


0%2B8=8 Multiply


8=8 Add


8=8 Reduce. Since this equation is true the solution works.


So the solution (0,4) satisfies 3%2Ax%2B2%2Ay=8


Since the solution (0,4) satisfies the system of equations


-3%2Ax%2B2%2Ay=8
3%2Ax%2B2%2Ay=8


this verifies our answer.