SOLUTION: what is the solution to- 9x-3y=3 3X+8Y=-17

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Question 111901: what is the solution to- 9x-3y=3
3X+8Y=-17
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

9%2Ax-3%2Ay=3
3%2Ax%2B8%2Ay=-17

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

-3%2Ay=3-9%2AxSubtract 9%2Ax from both sides

y=%283-9%2Ax%29%2F-3 Divide both sides by -3.


Which breaks down and reduces to



y=-1%2B3%2Ax Now we've fully isolated y

Since y equals -1%2B3%2Ax we can substitute the expression -1%2B3%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


3%2Ax%2B8%2Ahighlight%28%28-1%2B3%2Ax%29%29=-17 Replace y with -1%2B3%2Ax. Since this eliminates y, we can now solve for x.

3%2Ax%2B8%2A%28-1%29%2B8%283%29x=-17 Distribute 8 to -1%2B3%2Ax

3%2Ax-8%2B24%2Ax=-17 Multiply



3%2Ax-8%2B24%2Ax=-17 Reduce any fractions

3%2Ax%2B24%2Ax=-17%2B8Add 8 to both sides


3%2Ax%2B24%2Ax=-9 Combine the terms on the right side



27%2Ax=-9 Now combine the terms on the left side.


cross%28%281%2F27%29%2827%2F1%29%29x=%28-9%2F1%29%281%2F27%29 Multiply both sides by 1%2F27. This will cancel out 27%2F1 and isolate x

So when we multiply -9%2F1 and 1%2F27 (and simplify) we get



x=-1%2F3 <---------------------------------One answer

Now that we know that x=-1%2F3, lets substitute that in for x to solve for y

3%28-1%2F3%29%2B8%2Ay=-17 Plug in x=-1%2F3 into the 2nd equation

-1%2B8%2Ay=-17 Multiply

8%2Ay=-17%2B1Add 1 to both sides

8%2Ay=-16 Combine the terms on the right side

cross%28%281%2F8%29%288%29%29%2Ay=%28-16%2F1%29%281%2F8%29 Multiply both sides by 1%2F8. This will cancel out 8 on the left side.

y=-16%2F8 Multiply the terms on the right side


y=-2 Reduce


So this is the other answer


y=-2<---------------------------------Other answer


So our solution is

x=-1%2F3 and y=-2

which can also look like

(-1%2F3,-2)

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

9%2Ax-3%2Ay=3
3%2Ax%2B8%2Ay=-17

we get


graph of 9%2Ax-3%2Ay=3 (red) and 3%2Ax%2B8%2Ay=-17 (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%2F3,-2). This verifies our answer.


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Check:

Plug in (-1%2F3,-2) into the system of equations


Let x=-1%2F3 and y=-2. Now plug those values into the equation 9%2Ax-3%2Ay=3

9%2A%28-1%2F3%29-3%2A%28-2%29=3 Plug in x=-1%2F3 and y=-2


-9%2F3%2B6=3 Multiply


9%2F3=3 Add


3=3 Reduce. Since this equation is true the solution works.


So the solution (-1%2F3,-2) satisfies 9%2Ax-3%2Ay=3



Let x=-1%2F3 and y=-2. Now plug those values into the equation 3%2Ax%2B8%2Ay=-17

3%2A%28-1%2F3%29%2B8%2A%28-2%29=-17 Plug in x=-1%2F3 and y=-2


-3%2F3-16=-17 Multiply


-51%2F3=-17 Add


-17=-17 Reduce. Since this equation is true the solution works.


So the solution (-1%2F3,-2) satisfies 3%2Ax%2B8%2Ay=-17


Since the solution (-1%2F3,-2) satisfies the system of equations


9%2Ax-3%2Ay=3
3%2Ax%2B8%2Ay=-17


this verifies our answer.