Question

form the pair of linear equations for the following problem and find their solutions by substitution method.
I) the difference between two numbers is 26 and one number is three times the other find them​

Answer 1

Let :

• First Number= x
• Second number = y
• x > y

Given :

• Difference between two Number = 26
• First Number is three times the second number

To find :

Two Number by substitution method.

Solution :

Case 1)

Difference between two Number = 26

x - y = 26 ....... equation 1

Case 2)

First Number is three times the second number

x = 3y ....... equation 2

Put , value of x from equation 2 , into equation 1

(3y) - y = 26

2y = 26

y = 26 ÷ 2

y = 13

Now. put value of y in equation 2

x = 3(13)

x = 39

ANSWER :

• Linear equation are

1. x - y = 26
2. x = 3y

• Two Number are

1. x = 39
2. y = 13

Answer 2

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Let the two numbers be x and y respectively, such that y > x.

According to the question,

y = 3x ……………… (1)

y – x = 26 …………..(2)

Substituting the value of (1) into (2), we get

3x – x = 26

x = 13 ……………. (3)

Substituting (3) in (1), we get y = 39

Hence, the numbers are 13 and 39.

(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Solution:

Let the larger angle by xo and smaller angle be yo.

We know that the sum of two supplementary pair of angles is always 180o.

According to the question,

x + y = 180o……………. (1)

x – y = 18o ……………..(2)

From (1), we get x = 180o – y …………. (3)

Substituting (3) in (2), we get

180o – y – y =18o

162o = 2y

y = 81o ………….. (4)

Using the value of y in (3), we get

x = 180o – 81o

= 99o

Hence, the angles are 99o and 81o.