If (X, Y) Is A Solution To The System Of Equations, What Is The Value Of Y? 1 4 X + 1 8 Y = 2 1 3 X + 1 2 Y = 4

If (x, y) is a solution to the system of equations, what is the value of y? 1 4 x + 1 8 y = 2 1 3 x + 1 2 y = 4

Answer:

Step-by-step explanation:

Equation (A):

14x + 18y = 2

18y = -14x + 2

(1/18) 18y = -14x + 2 (1/18)

y = -7x/9 + 1/9

Equation (B):

13x + 12y = 4

12y = -13x + 4

(1/12) 12y = -13x + 4 (1/12)

y = -13x/12 + 1/3

Equate in terms of x to find the value of x:

-7x/9 + 1/9 = -13x/12 + 1/3

13x/12 - 7x/9 = 1/3 - 1/9

39x/36 - 28x/36 = 12/36 - 4/36 ⇒ Convert to similar terms with LCM=36

11x/36 = 8/36

(36/11) 11x/36 = 8/36 (36/11)

x = 8/11

Find y by substituting x = 8/11:

y = -7x/9 + 1/9

y = -7(8/11)(1/9) + 1/9

y = -56/99 + 11/99

y = -45/99

y = - 5/11

OR:

y = -13x/12 + 1/3

y = -13(8/11)(1/12) + 1/3

y = -104/132 + 44/132

y = -60/132

y = - 5/11

The solution (x, y) is (8/11, -5/11) where:

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