SOLUTION: 1)Solve by substitution method 7x+3y= -28 -2x +y =21 2)solve by sustitution method 2m +n = -7 m - 8m = 73

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Question 131028: 1)Solve by substitution method
7x+3y= -28
-2x +y =21
2)solve by sustitution method
2m +n = -7
m - 8m = 73
3)solve by substitution method
3x - 6y= -30
9x + 124= y
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started



# 1




Start with the given system of equations:

system%287x%2B3y=-28%2C-2x%2By=21%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

7x%2B3y=-28 Start with the first equation


3y=-28-7x Subtract 7x from both sides


3y=-7x-28 Rearrange the equation


y=%28-7x-28%29%2F%283%29 Divide both sides by 3


y=%28%28-7%29%2F%283%29%29x%2B%28-28%29%2F%283%29 Break up the fraction


y=%28-7%2F3%29x-28%2F3 Reduce



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

Since y=%28-7%2F3%29x-28%2F3, we can now replace each y in the second equation with %28-7%2F3%29x-28%2F3 to solve for x



-2x%2Bhighlight%28%28%28-7%2F3%29x-28%2F3%29%29=21 Plug in y=%28-7%2F3%29x-28%2F3 into the first equation. In other words, replace each y with %28-7%2F3%29x-28%2F3. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



%283%29%28-2x-%287%2F3%29x-28%2F3%29=%283%29%2821%29 Multiply both sides by the LCM of 3. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



-6x-7x-28=63 Distribute and multiply the LCM to each side



-13x-28=63 Combine like terms on the left side


-13x=63%2B28Add 28 to both sides


-13x=91 Combine like terms on the right side


x=%2891%29%2F%28-13%29 Divide both sides by -13 to isolate x



x=-7 Divide





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


So the first part of our answer is: x=-7









Since we know that x=-7 we can plug it into the equation y=%28-7%2F3%29x-28%2F3 (remember we previously solved for y in the first equation).



y=%28-7%2F3%29x-28%2F3 Start with the equation where y was previously isolated.


y=%28-7%2F3%29%28-7%29-28%2F3 Plug in x=-7


y=49%2F3-28%2F3 Multiply


y=7 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=7









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

So our answers are:

x=-7 and y=7

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 7x%2B3y=-28 (red) and -2x%2By=21 (green) and the intersection of the lines (blue circle).










Start with the given system of equations:

system%282m%2Bn=-7%2Cm-8m=73%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 n.




So let's isolate n in the first equation

2m%2Bn=-7 Start with the first equation


n=-7-2m Subtract 2m from both sides


n=-2m-7 Rearrange the equation


n=%28-2m-7%29%2F%281%29 Divide both sides by 1


n=%28%28-2%29%2F%281%29%29m%2B%28-7%29%2F%281%29 Break up the fraction


n=-2m-7 Reduce



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

Since n=-2m-7, we can now replace each n in the second equation with -2m-7 to solve for m



m-8m=73 Plug in n=-2m-7 into the first equation. In other words, replace each n with -2m-7. Notice we've eliminated the n variables. So we now have a simple equation with one unknown.



m%2B%28-8%29%28-2%29m%2B%28-8%29%28-7%29=73 Distribute -8 to -2m-7


m%2B16m%2B56=73 Multiply


17m%2B56=73 Combine like terms on the left side


17m=73-56Subtract 56 from both sides


17m=17 Combine like terms on the right side


m=%2817%29%2F%2817%29 Divide both sides by 17 to isolate m



m=1 Divide





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


So the first part of our answer is: m=1









Since we know that m=1 we can plug it into the equation n=-2m-7 (remember we previously solved for n in the first equation).



n=-2m-7 Start with the equation where n was previously isolated.


n=-2%281%29-7 Plug in m=1


n=-2-7 Multiply


n=-9 Combine like terms



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


So the second part of our answer is: n=-9









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

So our answers are:

m=1 and n=-9

which form the point (note: simply replace m with x and replace n with y)








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 2m%2Bn=-7 (red) and m-8m=73 (green) and the intersection of the lines (blue circle).