SOLUTION: Solve by the elimination method. 4a+9b=8 -4a+b=32 Determine the solution of the system. Select the correct choice below​ and, if​ necessary, fill in the answe

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Question 1101944: Solve by the elimination method.
4a+9b=8
-4a+b=32
Determine the solution of the system. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.The solution is ? (type an ordered pair)
or
B.There are infinitely many solutions.
or
C.There is no solution.

Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Slopes are not the same, so you know there is ONE solution. Part of the elimination process is already setup for you, to eliminate a and find b.

The other variable you find using ...
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Adding the two given equations eliminates a, giving you



Then substituting a=4 in either of the equations, you can solve for b.

The answer is A: there is a solution.

You can finish the work to find it.
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
Add the two equations. The terms "4a" and "-4a" will cancel each other, and you will get a single equation for one unknown "b" :

9b + b = 8 + 32,   or


10b = 40  ====>  b =  = 4.    (It is how the Elimination method works)


Then from the second of the two given equations you can determine "a":


-4a + 4 = 32  ====>  4a = 4 - 32  ====>  4a = -28  ====>  a =  = -7.


The given system has the unique solution, and this solution is   a= -7,  b= 4,  or  (a,b) = (-7,4).


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