# Solve the following pair of linear equations by the elimination method and the substitution method: x + y = 5 and 2x – 3y = 4 - Mathematics

Solve the following pair of linear equations by the elimination method and the substitution method:

x + y = 5 and 2x – 3y = 4

#### Solution

x + y =5 and 2x –3y = 4

By elimination method

x + y =5 ... (i)

2x –3y = 4 ... (ii)

Multiplying equation (i) by (ii), we get

2x + 2y = 10 ... (iii)

2x –3y = 4 ... (ii)

Subtracting equation (ii) from equation (iii), we get

5y = 6

y = 6/5

Putting the value in equation (i), we get

x = 5 - (6/5) = 19/5

Hence, x = 19/5 and y = 6/5

By substitution method

x + y = 5 ... (i)

Subtracting y both side, we get

x = 5 - y ... (iv)

Putting the value of x in equation (ii) we get

2(5 – y) – 3y = 4

-5y = - 6

y = -6/-5 = 6/5

Putting the value of y in equation (iv) we get

x = 5 – 6/5

x = 19/5

Hence, x = 19/5 and y = 6/5 again

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Elimination Method
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Chapter 3: Pair of Linear Equations in Two Variables - Exercise 3.4 [Page 56]

#### APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.4 | Q 1.1 | Page 56

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