Question 1102068
let x = john's age.
let y = jasmine's age.


x + y = 4x


solve for y to get y = 3x.


no matter how old john is, jasmine will be 3 times as old, and the sum of their ages will be 4 times john's age.


for example:


if john is 1 years old, then jasmine is 3 years old and the sum of their ages is 4 which is 4 times john's age.


if john is 5 years old, then jasmine is 15 years old and the sum of their ages is 20 which is 4 times john's age.


you cannot determine john's age from this formula because john could be any age between any number greater than 0 and some finite number such as the maximum age that jasmine can be.


for example:


if john is 1/3 years old, then jasmine is 1 year old and the sum of their ages is 4/3 which if 4 times john's age.


what you have is a system of equations where the result is 0 = 0.
this means you have an infinite number of possible solutions.


consider.


x + y = 4x
y = 3x


that's your system of equations that has to be solved simultaneously.


rearrange the equations as follows:


start with x + y = 4x
subtract 4x from both sides of the equation to get -3x + y = 0


start with y = 3x
subtract 3x from both sides of the equation to get -3x + y = 0


they're the same equation which results in an infinite number of solutions.


any solution of the first equation is also a solution of the second equation.