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# What is the solution of the equations $x + y = 3$, $3x - 2y = 4$.${\text{A}}{\text{. }}x = 2,y = 1 \\ {\text{B}}{\text{. }}x = 1,y = 2 \\ {\text{C}}{\text{. }}x = - 2,y = 1 \\ {\text{D}}{\text{. }}x = - 2,y = - 1 \\$

Last updated date: 16th Mar 2023
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Hint- Here, we will be solving the given two equations in two variables (i.e., x and y) with the help of elimination method which requires the coefficients of all the variables except one variable whose value is needed to be the same.

The given linear equations are $x + y = 3{\text{ }} \to {\text{(1)}}$ and $3x - 2y = 4{\text{ }} \to {\text{(2)}}$
$3\left( {x + y} \right) = 3 \times 3 \\ \Rightarrow 3x + 3y = 9{\text{ }} \to {\text{(3)}} \\$
$\Rightarrow 3x + 3y - \left( {3x - 2y} \right) = 9 - 4 \\ \Rightarrow 3x + 3y - 3x + 2y = 5 \\ \Rightarrow 5y = 5 \\ \Rightarrow y = 1 \\$
$x + 1 = 3 \\ \Rightarrow x = 2 \\$