SOLUTION: Find values for m and b in the following system so that the solution to the system is (-3,4) 5x+7y=b mx+y=22

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Question 111979: Find values for m and b in the following system so that the solution to the system is (-3,4)
5x+7y=b
mx+y=22
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Find values for m and b in the following system so that the solution to the system is (-3,4)
5x%2B7y=b
mx%2By=22
Since (x,y) = (-3,4), we will have:


5%2A%28-3%29+%2B+7%2A4+=+b
m%2A%28-3%29+%2B+4+=+22
--------------------------
-+15+%2B+28+=+b…………..=> b+=+13
-3m+%2B+4+=+22…………..=> -3m+=+22+%96+4…….=>-3m+=+18….=> m+=+18%2F%28-3%29…..=> m+=+-6
Check:
From the graph we can see that the intersection is (-3, 4).
This means the+solution is (-3, 4) which means x=-3 and y=4.

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


5x%2B7y=13

-6x%2By=22





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


5x%2B7y=13 Start with the given equation



7y=13-5x Subtract 5+x from both sides



7y=-5x%2B13 Rearrange the equation



y=%28-5x%2B13%29%2F%287%29 Divide both sides by 7



y=%28-5%2F7%29x%2B%2813%29%2F%287%29 Break up the fraction



y=%28-5%2F7%29x%2B13%2F7 Reduce



Now lets graph y=%28-5%2F7%29x%2B13%2F7 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-5%2F7%29x%2B13%2F7%29+ Graph of y=%28-5%2F7%29x%2B13%2F7




So let's solve for y on the second equation


-6x%2By=22 Start with the given equation



1y=22%2B6x Add 6+x to both sides



1y=%2B6x%2B22 Rearrange the equation



y=%28%2B6x%2B22%29%2F%281%29 Divide both sides by 1



y=%28%2B6%2F1%29x%2B%2822%29%2F%281%29 Break up the fraction



y=6x%2B22 Reduce





Now lets add the graph of y=6x%2B22 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-5%2F7%29x%2B13%2F7%2C6x%2B22%29+ Graph of y=%28-5%2F7%29x%2B13%2F7(red) and y=6x%2B22(green)


From the graph, we can see that the two lines intersect at the point (-3,4) (note: you might have to adjust the window to see the intersection)