# 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 \\

$

Answer

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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.

“Complete step-by-step answer:”

The given linear equations are $x + y = 3{\text{ }} \to {\text{(1)}}$ and $3x - 2y = 4{\text{ }} \to {\text{(2)}}$

Here, we will solve these two equations for the values of variables x and y with the help of elimination method.

For this, we will make the coefficient of variable x in both the given equation (1) and (2) same. This will result in the value of y and then by substituting back this value of variable y in any of the given equations, we will obtain the value of variable x.

Multiplying equation (1) by 3 on both sides, we get

$

3\left( {x + y} \right) = 3 \times 3 \\

\Rightarrow 3x + 3y = 9{\text{ }} \to {\text{(3)}} \\

$

Subtracting equation (2) from equation (3), we have

$

\Rightarrow 3x + 3y - \left( {3x - 2y} \right) = 9 - 4 \\

\Rightarrow 3x + 3y - 3x + 2y = 5 \\

\Rightarrow 5y = 5 \\

\Rightarrow y = 1 \\

$

Putting y=1 in equation (1), we get

$

x + 1 = 3 \\

\Rightarrow x = 2 \\

$

Therefore, the solution of the given two equations is x=2, y=1.

Hence, option A is correct.

Note- In these types of problems, the two given equations in two variables can also be solved with the help of substitution method. In this method, the value of one variable (let us say x) is represented in terms of another variable (i.e. y) using the first equation and then we will substitute this in the second equation.

“Complete step-by-step answer:”

The given linear equations are $x + y = 3{\text{ }} \to {\text{(1)}}$ and $3x - 2y = 4{\text{ }} \to {\text{(2)}}$

Here, we will solve these two equations for the values of variables x and y with the help of elimination method.

For this, we will make the coefficient of variable x in both the given equation (1) and (2) same. This will result in the value of y and then by substituting back this value of variable y in any of the given equations, we will obtain the value of variable x.

Multiplying equation (1) by 3 on both sides, we get

$

3\left( {x + y} \right) = 3 \times 3 \\

\Rightarrow 3x + 3y = 9{\text{ }} \to {\text{(3)}} \\

$

Subtracting equation (2) from equation (3), we have

$

\Rightarrow 3x + 3y - \left( {3x - 2y} \right) = 9 - 4 \\

\Rightarrow 3x + 3y - 3x + 2y = 5 \\

\Rightarrow 5y = 5 \\

\Rightarrow y = 1 \\

$

Putting y=1 in equation (1), we get

$

x + 1 = 3 \\

\Rightarrow x = 2 \\

$

Therefore, the solution of the given two equations is x=2, y=1.

Hence, option A is correct.

Note- In these types of problems, the two given equations in two variables can also be solved with the help of substitution method. In this method, the value of one variable (let us say x) is represented in terms of another variable (i.e. y) using the first equation and then we will substitute this in the second equation.

Last updated date: 15th Sep 2023

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