o + y = 21
o = 7 + 6 y
so
7 + 7y = 21
y = 2
o = 7 + 6 y
so
7 + 7y = 21
y = 2
According to the problem, the older person is seven years older than six times the age of the younger person. We can express this information with the equation:
y = 6x + 7
The sum of their ages is given as 21, so we can write another equation:
x + y = 21
Now, we have a system of two equations with two variables. We can solve this system using either substitution or elimination method. Let's use the substitution method:
Substitute the value of y from the first equation into the second equation:
x + (6x + 7) = 21
Combine like terms:
7x + 7 = 21
Now, isolate the variable:
7x = 21 - 7
7x = 14
Divide both sides by 7:
x = 2
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y:
y = 6x + 7
y = 6(2) + 7
y = 12 + 7
y = 19
Therefore, the younger person is 2 years old, and the older person is 19 years old.