Question

the sum of thrice the first number, second number and twice the third number is 5.if thrice the second number is subtracted from the sum of first number and thrice the the third we get 2.if the third number is subtracted from the sum of twice the first , thrice the second we get 1 .find the numbers​

Answer 1

Answer:

Numbers are 22 and 40.

Step-by-step explanation:

Let us assume, the two numbers are x and y.

Given:

3x + y = 142 ------------1

And also given:

4x – y = 138

y = 4x – 138 --------------2

Substitute the value of y from eqn 2 in eqn 1

3x + 4x – 138 = 142

7x - 138 = 142

7x = 142 + 138

7x = 280

x = 40

Therefore, y = (4 * 40) – 138 = 22

The two numbers are 40 and 22

Answer 2

Answer:

Let the three numbers be x, y, z

From the given data we get the following equations,

3 2 x y + + z = 5 …(1) x z + = 3 3y 2– …(2) 2 3 x y + = – z 1 …(3)

(1) × 1 ------ 3 2 x y + + z = 5

                                                (-)

(2) × 3 ----- 3 9 x y – + 9z = 6  

                   10y – 7z = –1 …(4)  

(1) × 2 Þ 624 x y + + z = 10

(3) ×3 Þ 6 9 x y + − 3z = 3 (−)

− + 7 7 y z = 7 …(5)

Adding (4) and (5), 10 7 y z – = –1

− + 7 7 y z = 7

3y = 6 Þ y = 2

Substituting y = 2 in (5),− + 14 7z = 7 Þz = 3

Substituting y = 2 and z = 3 in (1),  

3 2 x + + 6 = 5 we get ⇒ =x −1

Therefore, x = –1, y = 2, z= 3