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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