Question

13. If 5x + 7y = 17 and 7x + 5y = 19,
then what is the value of x-y?*
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Answer 1

Given :-

• 5x + 7y = 17 ----- [Equation 1]
• 7x + 5y = 19 ------ [Equation 2]

To find :-

x - y = ?

Solution :-

We shall solve this question by first adding the 2 equations.

(Equation 1) + (Equation 2)

5x + 7y = 17

{+} 7x + 5y = 19

12x + 12y = 36

→ 12x + 12y = 36

→ 12(x + y) = 36

→ x + y = 36 ÷ 12

→ x + y = 3 ------ [Equation 3]

Now let's subtract Equation 2 from Equation 1

(Equation 1) - (Equation 2)

5x + 7y = 17

{-} 7x + 5y = 19

-2x + 2y = -2

→ 2y - 2x = -2

→ 2(y - x) = -2

→ y - x = -1

→ -x + y = -1 ------ [Equation 4]

Adding Equation 3 and Equation 4,

(Equation 3) + (Equation 4)

x + y = 3

{+} -x + y = -1

2y = 3 - 1

→ 2y = 2

→ y = 2 ÷ 2

∴ y = 1

Substitute the value of y in Equation 1 to find the value of x.

x + y = 3

→ x + 1 = 3

→ x = 3 - 1

∴ x = 2

For finding (x - y)

x - y = 2 - 1

→ x - y = 1