SOLUTION: solve the system by substitution 9x+8y=4, 8x-8y=-72

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Question 549857: solve the system by substitution 9x+8y=4, 8x-8y=-72
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=4%2C8x-8y=-72%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=4 Start with the first equation


8y=4-9x Subtract 9x from both sides


8y=-9x%2B4 Rearrange the equation


y=%28-9x%2B4%29%2F%288%29 Divide both sides by 8


y=%28%28-9%29%2F%288%29%29x%2B%284%29%2F%288%29 Break up the fraction


y=%28-9%2F8%29x%2B1%2F2 Reduce



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

Since y=%28-9%2F8%29x%2B1%2F2, we can now replace each y in the second equation with %28-9%2F8%29x%2B1%2F2 to solve for x



8x-8highlight%28%28%28-9%2F8%29x%2B1%2F2%29%29=-72 Plug in y=%28-9%2F8%29x%2B1%2F2 into the second equation. In other words, replace each y with %28-9%2F8%29x%2B1%2F2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



8x%2B%28-8%29%28-9%2F8%29x%2B%28-8%29%281%2F2%29=-72 Distribute -8 to %28-9%2F8%29x%2B1%2F2


8x%2B%2872%2F8%29x-8%2F2=-72 Multiply


%288%29%288x%2B%2872%2F8%29x-8%2F2%29=%288%29%28-72%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)



64x%2B72x-32=-576 Distribute and multiply the LCM to each side



136x-32=-576 Combine like terms on the left side


136x=-576%2B32Add 32 to both sides


136x=-544 Combine like terms on the right side


x=%28-544%29%2F%28136%29 Divide both sides by 136 to isolate x



x=-4 Divide





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


So the first part of our answer is: x=-4









Since we know that x=-4 we can plug it into the equation y=%28-9%2F8%29x%2B1%2F2 (remember we previously solved for y in the first equation).



y=%28-9%2F8%29x%2B1%2F2 Start with the equation where y was previously isolated.


y=%28-9%2F8%29%28-4%29%2B1%2F2 Plug in x=-4


y=36%2F8%2B1%2F2 Multiply


y=5 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=5









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

So our answers are:

x=-4 and y=5

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=4 (red) and 8x-8y=-72 (green) and the intersection of the lines (blue circle).