"To calculate: The numbers when the difference of..." was answered by students like you

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

Isaiah Alsup

Answered question

2021-11-19

To calculate: The numbers when the difference of two positive numbers is 3 and the difference of their squares is 33.

Answer & Explanation

soniarus7x

Beginner2021-11-20Added 17 answers

It is provided that the difference of two positive numbers is 3 and the difference of their squares is 33.
Consider one number be x and the other number be y.
The system of equations in two variables thus becomes:

x - y = 3 \dots (1)

And,

x^{2} - y^{2} = 33 \dots (2)

Consider equation (1) and find the value of x:

x - y = 3

x = 3 + y

Substitute

3 + y

for xin equation (2) and solve for y:

{(3 + y)}^{2} - y^{2} = 33

9 + y^{2} + 6 y - y^{2} = 33

6 y = 24

y = 4

Now, substitute 4 for yin equation (1) and solve for x:

x - 4 = 3

x = 7

Therefore, the numbers are 7 and 4.

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