Find the solution for the following pair of equations
$2 y + x = 4$
$3 y - \frac{1}{2} x = 2$

(1, 2)

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(2, 1)

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(0, 2)

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(2, 3)

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Solution

The correct option is B $(2, 1)$
Given,
$2 y + x = 4 \Rightarrow x = 4 - 2 y \dots (i)$
and $3 y - \frac{1}{2} x = 2 \dots (i i)$

Step 1: Find the value of y
Substituting $x = 4 - 2 y$ in $(i i),$ we get
Equation $(i i)$ $\to$ $3 y - \frac{1}{2} (x) = 2$
$3 y - \frac{1}{2} (4 - 2 y) = 2$
$\Rightarrow 3 y - 2 + y = 2 \Rightarrow 4 y = 2 + 2 \Rightarrow 4 y = 4 \Rightarrow y = 1$

Step 2: Now, Find the value of x
Substitute $y = 1$ in equation $(i)$
Equation $(i)$ $\to$ $x = 4 - 2 (y)$
$x = 4 - 2 (1)$
$\Rightarrow x = 4 - 2 = 2$
$∴ x = 2, y = 1$

$∴$ Required solution for the given pair of equations is $(2, 1)$

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