Question

2X+Y-11=0,X-Y-1=0 substitution method

Answer 1

$\large\underline{\bold{Given \:Question - }}$

Solve the following equations by substitution method:-

2x + y - 11 = 0

and

x - y - 1 = 0.

$\large\underline{\bold{Solution-}}$

Method of Substitution :-

To solve systems using substitution, the following procedure is followed :-

Select one equation and solve it for one of its variables.

In the other equation, plug in or substitute for the variable just solved in previous step.

Solve the new equation in one variable to get its value.

Substitute the value found into any equation involving both variables and solve for the other variable.

Let's solve the problem now!!

Now, given linear equations are

2x + y - 11 = 0 -----(1)

and

x - y - 1 = 0 ----(2)

Step :- 1

From, equation (2), get the value of y in terms of x.

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

Step :- 2

Now, Substitute the value of 'y' evaluated in Step 1 in equation (1), we get

2x + x - 1 - 11 = 0

3x - 12 = 0

3x = 12

$\therefore \: \: \boxed{ \tt{x \: = \: 4}}$

Step :- 3

Now, Substitute the value of 'x' evaluated in Step - 2, in equation (3), we get

y = 4 - 1

$\therefore \: \boxed{ \tt{y \: = \: 3}}$

Hence,

x = 4 and y = 3 is the solution of given Pair of Linear Equations.

Answer 2

$\huge\bf\purple{\mathfrak{Given question}}$

Solve the following equations by substitution method:-

2x + y - 11 = 0

and

x - y - 1 = 0.

$\large\underline{\bold{Solution-}} </p><p>Solution−$

Method of Substitution :-

To solve systems using substitution, the following procedure is followed :-

Select one equation and solve it for one of its variables.

In the other equation, plug in or substitute for the variable just solved in previous step.

Solve the new equation in one variable to get its value.

Substitute the value found into any equation involving both variables and solve for the other variable.

Let's solve the problem now!!

Now, given linear equations are

2x + y - 11 = 0 -----(1)

and

x - y - 1 = 0 ----(2)

Step :- 1

From, equation (2), get the value of y in terms of x.

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

Step :- 2

Now, Substitute the value of 'y' evaluated in Step 1 in equation (1), we get

2x + x - 1 - 11 = 0

3x - 12 = 0

3x = 12

$\therefore \: \: \boxed{ \tt{x \: = \: 4}}∴$

x=4

Step :- 3

Now, Substitute the value of 'x' evaluated in Step - 2, in equation (3), we get

y = 4 - 1

$\therefore \: \boxed{ \tt{y \: = \: 3}}∴$

y=3

Hence,

x = 4 and y = 3 is the solution of given Pair of Linear Equations.