Question

solve the following pair of linear equation by the substitution method : 2x - y = 1, 4x + 3y = 27

Answer 1

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

Substituting Equation (1) in Equation 4x+3y=27


4x+3y=27
4x+3(2x+1)=27
4x+6x+3=27
10x=24
x=12/5

Now Substituting x=12/5 in any Equation

2*12/5 - y = 1. ( Equate the Equation)
y= 14/5

Answer 2

Concept:

Solution of linear equations by substitution method: In this method, we find out the value of one variable from one equation and substitute it in the second equation and then solve it to get the value of both variables.

Given:

The given linear equations are,

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

4x + 3y = 27       ----------------------- (ii)

Find:

The solution of the given set of equations, i.e., the values of x and y.

Answer:

The value of x is 3.

The value of y is 5.

Solution:

Taking equation (i), we get

2x - y = 1

2x = 1 + y

1 + y = 2x

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

Substituting this value of y from (a) in equation (ii), we get

4x + 3y = 27

4x + 3(2x - 1) = 27                  [From (a)]

4x + 6x - 3 = 27

10x = 27 + 3

10x = 30

x = 30/10

x = 3

Now, putting the value of x in (a), we get

y = 2x - 1

y = 2(3) - 1

y = 6 - 1

y = 5

Hence, x = 3 and y = 5.

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