Question

the difference between two numbers is 9. the first number plus twice the other number is 27. find the two numbers

Answer 1

So,

Let's translate this into mathematical form.

x - y = 9
x + 2y = 27

Elimination by Addition
Divide both sides of the second equation by 2
$\frac{1}{2}x + y = 13 \frac{1}{2}$

Add the two equations together
$\frac{3}{2} x = \frac{45}{2}$

Multiply both sides by $\frac{2}{3}$
$x = \frac{90}{6} \ or \ 15$

Substitute
15 - y = 9

Subtract 15 from both sides
-y = -6
y = 6

Substitute
15 - 6 = 9
9 = 9 This checks.

15 + 2(6) = 27

Distribute
15 + 12 = 27
27 = 27 This also checks.

S = {(15,6)}

Answer 2

A-b=9    ......a=9+b
a+2b=27
(9+b)+2b=27
9+3b=27
3b=27-9
3b=18
b=6
a=9+b=6+9=15