SOLUTION: 4. 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

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 4. 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       Log On

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Question 123342: 4. 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 jim_thompson5910(28548) About Me  (Show Source):
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# 4

If we have the solution (-3,4) , this means that x=-3 and y=4

Let's solve for b:

5x%2B7y=b Start with the first equation

5%28-3%29%2B7%284%29=b Plug in x=-3 and y=4


-15%2B28=b Multiply 5 and -3 to get -15. Multiply 7 and 4 to get 28.

b=13 Add -15 to 28 to get 13


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So our first answer is b=13
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Now let's solve for m:

mx%2By=22 Start with the second equation

m%28-3%29%2B%284%29=22 Plug in x=-3 and y=4

-3m%2B4=22 Multiply m and -3 to get -3m.

-3m=18 Subtract 4 from both sides

m=-6 Divide both sides by -3


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So our second answer is m=-6
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Summary:

So our answers are:
b=13 and m=-6