Question

Find the value of 5a-3b when a=7 and b =2

Answer 1

$\small{ \textsf{ \textbf{ \color{lime}{I SOLVE IT}}}}$

At first sight this seems impossible because there are TWO variables but only ONE equation. To solve for two variables we would normally require two equations. The no: of solutions would be finite.

Nevertheless; THIS problem CAN BE SOLVED but with an infinite number of solutions.

The following is one method out of several that can be used to find values of ‘a’ and ‘b’ such that ‘a’ and ‘b’ are WHOLE NUMBERS

Step 1:

Think of multiples of 3 such that when you add 1 the answer becomes a multiple of 5.

3no; 6no; 9YES (because 9+1=10, This is a multiple of 5); 12no, 15no, 18no 21no 24YES (because 24+1=25, this is a multiple of 5) etc..

Divide (the DERIVED multiple of 5) by 5. This gives you the value of ‘a’ as a WHOLE number

Step 2: To find the value of ‘b’, substitute the value of ‘a’ in the formula b=(5a-1)÷3

This equation is simply derived by making ‘b’ the subject of the original equation

Is there a way to solve for a and b in 5a-3b = 1 without trial and error?

At first sight this seems impossible because there are TWO variables but only ONE equation. To solve for two variables we would normally require two equations. The no: of solutions would be finite.

Nevertheless; THIS problem CAN BE SOLVED but with an infinite number of solutions.

The following is one method out of several that can be used to find values of ‘a’ and ‘b’ such that ‘a’ and ‘b’ are WHOLE NUMBERS

Step 1:

Think of multiples of 3 such that when you add 1 the answer becomes a multiple of 5.

3no; 6no; 9YES (because 9+1=10, This is a multiple of 5); 12no, 15no, 18no 21no 24YES (because 24+1=25, this is a multiple of 5) etc..

Divide (the DERIVED multiple of 5) by 5. This gives you the value of ‘a’ as a WHOLE number

Step 2: To find the value of ‘b’, substitute the value of ‘a’ in the formula b=(5a-1)÷3

This equation is simply derived by making ‘b’ the subject of the original equation

EXAMPLE 1:

9 is a multiple of 3 such that after adding 1 the answer (10) is a multiple of 5 .

10÷5=2 This is the value of ‘a’

Substitute a=2 in b=(5a-1)/3

b= (10 -1)/3

b= 9/3

b=3

Example 2:

24 is another multiple of 3 such that when 1 is added the answer, 25 is divisible by 5

So 25÷5 = 5 This is the value if ‘a’

After substitution: b= (25 - 1)/3

b=24/3

b=8