SOLUTION: Solve by using the substitution method 9x + 8y = -56 -2x + y = 18 What is the solution of the system?

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Question 157501: Solve by using the substitution method
9x + 8y = -56
-2x + y = 18
What is the solution of the system?
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%289x%2B8y=-56%2C-2x%2By=18%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

9x%2B8y=-56 Start with the first equation


8y=-56-9x Subtract 9x from both sides


8y=-9x-56 Rearrange the equation


y=%28-9x-56%29%2F%288%29 Divide both sides by 8


y=%28%28-9%29%2F%288%29%29x%2B%28-56%29%2F%288%29 Break up the fraction


y=%28-9%2F8%29x-7 Reduce



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

Since y=%28-9%2F8%29x-7, we can now replace each y in the second equation with %28-9%2F8%29x-7 to solve for x



-2x%2Bhighlight%28%28%28-9%2F8%29x-7%29%29=18 Plug in y=%28-9%2F8%29x-7 into the second equation. In other words, replace each y with %28-9%2F8%29x-7. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



%288%29%28-2x-%289%2F8%29x-7%29=%288%29%2818%29 Multiply both sides by the LCM of 8. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



-16x-9x-56=144 Distribute and multiply the LCM to each side



-25x-56=144 Combine like terms on the left side


-25x=144%2B56Add 56 to both sides


-25x=200 Combine like terms on the right side


x=%28200%29%2F%28-25%29 Divide both sides by -25 to isolate x



x=-8 Divide





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


So the first part of our answer is: x=-8









Since we know that x=-8 we can plug it into the equation y=%28-9%2F8%29x-7 (remember we previously solved for y in the first equation).



y=%28-9%2F8%29x-7 Start with the equation where y was previously isolated.


y=%28-9%2F8%29%28-8%29-7 Plug in x=-8


y=72%2F8-7 Multiply


y=2 Combine like terms and reduce. (note: if you need help with fractions, check out this solver)



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


So the second part of our answer is: y=2









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

So our answers are:

x=-8 and y=2

which form the point








Now let's graph the two equations (if you need help with graphing, check out this solver)


From the graph, we can see that the two equations intersect at . This visually verifies our answer.




graph of 9x%2B8y=-56 (red) and -2x%2By=18 (green) and the intersection of the lines (blue circle).