Question

15.If 2x+3y=7 and 3x+2y=3 then value of x+y=.....
(A)10 (B)4 (C)2(D)6​

Answer 1

Given:

• 2x + 3y = 7 → (Equation 1)
• 3x + 2y = 3 → (Equation 2)

To find:

1. x + y = ?

Method:

Adding the Equations 1 and 2,

2x + 3y = 7

(+) 3x + 2y = 3

5x + 5y = 10

⇒5(x + y) = 10

⇒ x + y = 2 → (Equation 3)

You can stop till here or continue solving to find values of x and y

Subtracting Equation 2 from 1,

2x + 3y = 7

(-) 3x + 2y = 3.

-x + y = 4

⇒y - x = 4 → (Equation 4)

Adding Equation 3 and 4,

x + y = 2

(+) -x + y = 4

2y = 6

⇒y = 6 ÷ 2

⇒y = 3

Substitute value of y in Equation 3,

x + y = 2

⇒x + 3 = 2

⇒x = 2 - 3

⇒x = -1

x + y = 2