Question

Aaron is 15 centimeters taller than Peter, and five times Aaron's height exceeds two times Peter's height by 525 centimeters. The system of linear equations that relates Aaron's height (x) and Peter's height (y) is given by . Aaron's height is centimeters, and Peter's height is centimeters.

Answer 1

The system of linear equations that relates Aaron's height (x) and Peter's height (y) is given by x - y = 15 and 5x - 2y = 525. Aaron's height is 165 centimeters, and Peter's height is 150 centimeters.

Explanation:

x-y=15

x=15+y find x

5(15+y)-2y=525 place x value in x placeholder

75+5y-2y=525 simplify

5y-2y=450 subtract 75 from both sides

3y=450 simplify

y=150

5x-2(150)=525 rewrite equation

5x-300=525 simplify

5x=825 add 300 to both sides

x=165

Answer 2

The system of linear equations that relates x and y:
x= 15 + y
5 x = 2 y+ 525
We will solve this system using substitution method:
5(15 + y)=2 y + 525
75 + 5 y = 2 y + 525
5 y - 2 y = 525 - 75
3 y = 450, y = 450 : 3 y = 150
x = 15 + y x = 15 + 150 x = 165
Answer: Aaron´s height is 165 cm and Peter´s height is 150 cm.