What is the solution of 3x + 8y = 92 and 2x - 6y = 16.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The set of linear equations 3x + 8y = 92 and 2x - 6y = 16 have to be solved.

3x + 8y = 92 ...(1)

2x - 6y = 16 ...(2)

2x - 6y = 16

=> x = 8 + 3y

Substitute in (1)

=> 3(8 + 3y) + 8y = 92

=> 24 + 9y + 8y = 92

=> 17y = 68

=> y = 4

x = 20

The solution of the given set of equations is x = 20, y = 4

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jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

3x + 8y = 92 

2x - 6y = 16

First multiply everything in the top equation by 2 and everything in the bottom equation by 3

By doing that, you should get

6x + 16y = 184

6x - 18y = 48 now subtract 6x with 6x (which means also subtract 16y with 18y and 184 with 48)

By subtracting, you should get

34y = 136 now divide both sides by 34

By dividing, you should get

y = 4 which is your answer for " y "

Now plug 4 into one of the equation

2x - 6 ( 4 )  = 16 Multiply -6 with 4

By multiplying, you should get

2x -24 = 16 now add 24 on both sides

By adding, you should get

2x = 40 now divide both sides by 2

By dividing, you should get

x = 20 which is your answer for " x "

So your answer is x = 20    ;   y = 4

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