Question

If 31x+43y=117 and 43x+31y=105 then what is the value of x-y

Answer 1

Answer: x - y = -1

Step-by-step explanation:

31x + 43y = 117 ——— 1.

43x + 31y = 105 ——— 2.

When we subtract 1. from 2., we get

12x - 12y = -12

=> x - y = -1

Therefore x - y = -1

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Answer 2

Given: 31x + 43y = 117 → 1

           43x + 31y = 105 → 2

To Find: x - y

Solution:

• Substracting equation 2 from equation 1:

31x + 43y = 117

43x + 31y = 105

-       -         -      

-12x + 12y = 12

12 (-x + y) = 12

y - x  =  12/12

y - x = 1

y = 1 + x → (3)

• Substituiting y in equation (2)

43x + 31 (1 + x) = 105

43x + 31 + 31x = 105

43x + 31x = 105 - 31

74x = 74

x = 74/74

x = 1

• Substituiting value of x in equation (3)

y = 1 + x =

y = 1 + 1

y = 2

Hence, x - y = 1 - 2 = -1