the sum of two numbers is three times the difference of the two numbers. the greatest number is five more than the lesser number.

Question

a)write a system of equations to represent this situation

b)solve simultaneously using the method of substitution or elimination in order to find the values of the lesser and greater numbers

Answer 1

Set up all the info you have to solve it.

first set up the problem:

let X be the bigger number

let Y be the smaller

NOW the info:

sum of two numbers that just means X + Y

difference of the two numbers that just means X - Y

SO one equations will be based on

the sum of two numbers is three times the difference of the two numbers that just means:

sum of two numbers equals 3 * difference of the two numbers

A second equation is based on:

the greatest number is five more than the lesser number just means that X is Y + 5.

form equations from that info I gave you. On the first equation combine terms (all the X's and Y's together); then since the second equation is already solved for X just substitute the second into the first and solve for Y.