# 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

•

Total views: 304.5k

•

Views today: 2.85k

Answer

Verified

304.5k+ views

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.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE