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Question

Solve the following pair of linear equations in two variables:
$$3=2x+y$$ and $$9 = 4x - y$$


Solution

Given:-
$$3 = 2x + y ..... \left( 1 \right)$$
$$9 = 4x - y ..... \left( 2 \right)$$

Adding equation $$\left( 1 \right) \& \left( 2 \right)$$, we have
$$3 + 9 = \left( 2x + y \right) + \left( 4x - y \right)$$
$$12 = 6x$$
$$\Rightarrow x = \cfrac{12}{6} = 2$$

Substituting the value of $$x$$ in equation $$\left( 1 \right)$$, we have
$$3 = 2 \times 2 + y$$
$$\Rightarrow y = 3 - 4 = -1$$

Hence the value of $$x$$ and $$y$$ are $$2$$ and $$-1$$ respectively.

Mathematics

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