A sum of two numbers is 16 three times the larger number decreased by the smaller number is 72 find the two numbers

Let a = the larger number
b = the smaller number

a + b = 16
3a - b = 72

a = 16 - b

3(16 - b) - b = 72

48 - 3b - b = 72

-4b = 24

b = -6

a = 16 - (-6)

a = 22

The two numbers are:
22 and -6

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AmitPaswan AmitPaswan · Answer 2 · 2022-07-29T15:37:31+02:00

The value of larger number is 22 and value of smaller number is -6 .

What is elimination method?

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

According to the question

Let larger number be = x

and smaller number be = y

A sum of two numbers is 16 .

i.e

x + y = 16 ------------------- (1)

Three times the larger number decreased by the smaller number is 72 .

i.e

3x - y = 72 ------------------- (2)

Now,

solving both equation by elimination method

Multiplying equation (1) by 3

to make equal coefficient for x

So, x can be eliminated

3(x + y)=16 * 3

3x + 3y = 48 -------------- (3)

Now,

subtracting equation (3) from equation (2)

3x - y = 72

-3x - 3y = -48

-4y = 24

y = -6

Putting value of x in eq(1)

x + y = 16

x - 6 = 16

x = 22

Hence, The value of larger number is 22 and value of smaller number is -6 .

To know more about elimination method here:

brainly.com/question/14619835

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