Question

If 5x+3y=12 and 3x-5y=6 then find x-y​

Answer 1

Step-by-step explanation:

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Answer 2

Given:

• 5x + 3y = 12 ----- [Equation 1]
• 3x - 5y = 6 ----- [Equation 2]

To find:

x - y = ?

Solution:

Adding Equation 1 and 2,

5x + 3y = 12

{+} 3x - 5y = 6

8x - 2y = 18

➥ 2(4x - y) = 18

⇒ 4x - y = 18 ÷ 2

⇒ 4x - y = 9 ------ [Equation 3]

Subtracting Equation 2 from Equation 1,

5x + 3y = 12

{-} 3x - 5y = 6

2x - 8y = 6

⇒ 2(x - 4y) = 6

➝ x - 4y = 6 ÷ 2

➝ x - 4y = 3 ----- [Equation 4]

If we are asked to find the value of x and y, follow the below steps:

Subtract Equation 4 from Equation 3

4x - y = 9

{-} x - 4y = 3

3x - 3y = 6

➥ 3x - 3y = 6

➝ 3(x - y) = 6

➝ x - y = 6 ÷ 3

∴ x - y = 2