Question

Is ( 1,2 ) a solution of the following pair of linear equations in two variables? x + 3y = 7 ,2x + y = 4

Answer 1

x+3y=7................ (1)

2x+y=4..........(2)

Multiplying equation (1) by 2 we get,

2x+6y=14........(3)

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

5y=10

y=10/5

y=2.

Substituting the value of y in (1) we get,

x+3y=7................ (1)

x+3×2=7

x+6=7

x=7-6

x=1

Therefore (1, 2) is the solution of the given pair of linear equations in two Variables.

Your Answer is right✔✔✔

Answer 2

Answer:

Yes, ( 1, 2 ) is the solution of the given pairs of linear equations.

Step-by-step-explanation:

We have to fine if ( 1, 2 ) is the solution of given pairs of linear equations.

The given linear equations are

x + 3y = 7 and

2x + y = 4

To check if ( 1, 2 ) is solution or not of given equations, we have to put x = 1 and y = 2 in the given equations.

x + 3y = 7 - - - ( 1 )

LHS = x + 3y

➞ LHS = 1 + 3 ( 2 )

➞ LHS = 1 + 6

➞ LHS = 7

RHS = 7

$\therefore\boxed{\red{\sf\:LHS\:=\:RHS}}$

Now, by substituting the given values of x and y in second equation, we get,

2x + y = 4 - - - ( 2 )

LHS = 2x + y

➞ LHS = 2 ( 1 ) + 2

➞ LHS = 2 + 2

➞ LHS = 4

RHS = 4

$\therefore\boxed{\red{\sf\:LHS\:=\:RHS}}$

( 1, 2 ) is the solution of the given pairs of linear equations.

Additional Information:

1. Linear Equations in two variables:

The equation with the highest index ( degree ) 1 is called as linear equation. If the equation has two different variables, it is called as 'linear equation in two variables'.

The general formula of linear equation in two variables is

ax + by + c = 0

Where, a, b, c are real numbers and

a ≠ 0, b ≠ 0.

2. Solution of a Linear Equation:

The value of the given variable in the given linear equation is called the solution of the linear equation