Solve the following pair of equations: 2x+y=7 3x+2y=12 Choose the correct answ

Question

Solve the following pair of equations:
$2 x + y = 7$
$3 x + 2 y = 12$
Choose the correct answer from the given options.

Options:

A . (2,3)

B . (3,2)

C . (1,0)

D . (-3,2)

Answer: Option A
:
A

We have,

$2 x + y = 7$ ...(1)
$3 x + 2 y = 12$ ...(2)

Multiply equation (1) by 2, we get:

$2 (2 x + y) = 2 (7)$
$\Rightarrow 4 x + 2 y = 14$ ...(3)

Subtracting (2) from (3) we get ,

$x = 2$
Substituting the value of $x$ in (1) we get,
$2 (2) + y = 7 ⟹ y = 3$

Thus, the solution for the given pair of linear equations is (2,3).

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