Given:
The system of equations is
To find:
The missing value for which the given system of equations have infinitely many solutions.
Solution:
Let the missing value be k.
We have,
Taking all the terms on the left side, the given equations can be rewritten as
The system of equations and
have infinitely many solutions if
We have,
Now,
On cross multiplication, we get
Therefore, the missing value is -10.
Answer:
8 years
Step-by-step explanation:
Let age of father be f
age of John be j
age of Alice be a
John's father is 5 times as old as John. We can write:
f = 5j
John is twice as old as Alice. We can write:
j = 2a
or
a = j/2
SUM OF ALL OF THEIR AGES (after 2 years) will be 58. We can write:
f+2 + j+2 + a+2 = 58
This becomes:
f + j + a + 6 = 58
f + j + a = 52
Now, we replace third equation with the first two (in bold) and get:
So John is 8 years old