Question

a + e=11
a2- f = 15
f + c = 6
ac -e 13​

Answer 1

• using f + c = 6

we have defined c because it has some value

thus the possible values of f are ;

• f ∈ { 1 , 2 , 3 , 4 , 5 }

To get a natural value of a ;

• we use f = 1

Therefore ;

• a² - f = 15
• a² = 16
• a = ± 4

At a = 4;

• a + e = 11
• e = 7

At a = -4

• a + e = 11
• e = 15

As we assumed f = 1 ;

Thus;

• f + c = 6
• c = 5

We have values of the variables.

So we use the last eq. to find the correct set of values.

ac - e = 13

# Set 1 ; a = 4 => e = 7

• LHS = (4)(5) - 7
• 13 = RHS

# Set 2 ; a = -4 => e = 15

• LHS = (-4)(5) - 15
• -20 - 15 ≠ 13
• THUS ≠ RHS .

Thus the second set of values will be discarded and so the values for these equations will be ;

• a = 4
• e = 7
• f = 1
• c = 5