Question

If 2x + y = 4 and 3x + y = 5, then the common solution for these two equations is .

[Use elimination method to solve]

• A. x = 1 and y = 2
• B. x = 2 and y = 1
• C. x = 0 and y = 4
• D. x = 2 and y = 0

Answer 1

The correct option is A x = 1 and y = 2

Given that,
Two equations are 2x + y = 4.....(1) and 3x + y = 5....(2)

Now,
Multiplying equation (1) with 3 and equation (2) with 2 to make the coefficients of x same in both equations, we get

3(2x + y = 4)
$\Rightarrow$ (6x + 3y = 12)....(3)

Similarly,
2(3x + y = 5)
$\Rightarrow$ (6x + 2y = 10)....(4)

Subtracting equation (4) from equation (3),
we get y = 2.

On putting y = 2 in the equation (1),
we get x = 1.