|
Question 118133: Find the values for m and b in the following system so that the solution to the system is (-3,4). 5x + 7y =b and mx + y =22. First; 5x+7y=b, =>5(-3)+7(4)=b,
=>-15+28=b, =>13=b. Now this one; mx + y=22; =>m(-3)+4=22, =>-3m=22-4=18,
=>-3m=18, =>m=18/(-3), =>m=-6. So then b=13 and m=-6.
I just want to know if I am correct please?
Thank you, Barb Neely
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You are correct.
.
A way you could convince yourself is to start with the equation set that you derived after
doing your work:
.
+5x + 7y = 13 and
-6x + y = 22
.
You could solve them simultaneously and see if the answers for x and y are (-3,4)
.
For example ... multiply the bottom equation (both sides, all terms) by -7 to make the equation
set become:
.
+5x + 7y = 13
42x - 7y = -154
.
Add these two equations together in vertical columns to make the terms containing y
cancel each other out and you end up with the "combined" equation of:
.
47x = -141
.
Solve for x by dividing both sides by 47 and you get that x = -3.
.
Next go back to one of the equations you developed and substitute -3 for x. If you do, you
find that y = +4. This being the case you can say that (-3, 4) is the common solution, just
as it should be ...
.
Or you could go to each of your derived equations one at a time ... and substitute -3
for x and +4 for y to see if each equation balances (left side equals right side) after
those substitutions. Both equations should balance ... as you might expect because you
are basically just following the process that you originally did to solve for b and m.
If both don't balance, then you would have to check your original work to find the error.
.
Good job of seeing your way through this problem ....
.
|
|
|
| |
