24 x + y = 48 6 x + y = 72 The solution to the given system of equations

Question

24 x + y = 48 6 x + y = 72 The solution to the given system of equations is ( x , y ) . What is the value of y ?

Accepted Answer

The correct answer is 80 . Subtracting the second equation in the given system from the first equation yields 24 x + y - 6 x + y = 48 - 72 , which is equivalent to 24 x - 6 x + y - y = - 24 , or 18 x = - 24 . Dividing each side of this equation by 3 yields 6 x = - 8 . Substituting - 8 for 6 x in the second equation yields - 8 + y = 72 . Adding 8 to both sides of this equation yields y = 80 . Alternate approach: Multiplying each side of the second equation in the given system by 4 yields 24 x + 4 y = 288 . Subtracting the first equation in the given system from this equation yields 24 x + 4 y - 24 x + y = 288 - 48 , which is equivalent to 24 x - 24 x + 4 y - y = 240 , or 3 y = 240 . Dividing each side of this equation by 3 yields y = 80 .

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