Question

Solve the following pair of linear equations by the substitution method.

(i) x + y = 14
x – y = 4

Answer 1

Required answer:-

Question:

◍ Solve the following pair of linear equations by the substitution method.

x + y = 14

x – y = 4

Solution:

Method used:

◍ Elimination by substitution

Procedure to understand the concept:

Steps:

1. From any of the given two equations, find the value of one variable in terms of the other.

2. Substitute the value of the variable, obtained in step(1), in the other equation and solve it.

3. Substitute the value of variable obtained in step(2), in the result of step (1) and get the value of remaining unknown variable.

Step by step explaination:

First calculate the value of y

That is,

x + y = 14

y = 14 - x

Now,

x - y = 4

x - (14 - x) = 4

x - 14 + x = 4

2x = 4 + 14

2x = 18

x = 9

As we came to knew the value of x as 9.

So, value of y:

y = 14 - x

y = 14 - 9

y = 5

Answer:

x = 9 and y = 5

Answer 2

Answer:

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Step-by-step explanation:

Let

x + y = 14 -----(1)

x – y = 4 ------(2)

From eq.(1) we get x = 14 - y -----(3)

Putting eq(3) in eq(2)

x - y = 4

(14 - y) - y = 4

14 - y - y = 4

14 - 2y = 4

14 - 4 = 2y

10 = 2y

y = 10 / 2

∴ y = 5

Putting y = 5 in eq(3)

x = 14 - y

x = 14 - 5

∴ x = 9

So the values are x = 9 and y = 5