Question

The sum of a number and twice another number is 17. The sum of twice the first number and the second number is 4. What are the two numbers?

a) define the variables

b) write a system of equations

c) solve by elimination

Answer 1

Explanation:

Given that,

a + 2b = 17

Also,

2a + b = 4

By adding the above expressions we get,

a + 2b + 2a + b = 17 + 4

3a + 3b = 21.

3 (a + b) = 21

a + b = 21/3

a + b = 7 Let us take 'b' = 10

a + 10 = 7

a = 7 - 10

a = -3

Now let's check by verifying by putting a = -3 and b = 10 in the previous expressions

a + 2b = 17

-3 + (2 × 10) = 17

-3 + 20 = 17

17 = 17

2a + b = 4

(2 × -3) + 10 = 4

-6 + 10 = 4

4 = 4

Therefore, a = -3 and b = 10 [(-3,10)] is the solution.