Question

The sum of three times a number and a second number is five. two times the first number added to the second number is 10. find the two numbers.

Answer 1

-5 , 20

Explanation:

Forming system of linear equations and solving:

Let x and y be the first and second number respectively.

3x + y = 5 -------------(i)

y = 5 - 3x

2x + y = 10 -------------(ii)

Method used for solving: substitution method.

Substitute y = 5 - 3x in equation (ii)

2x + 5 - 3x = 10

2x - 3x + 5 = 10

Combine like terms,

-x + 5 = 10

Subtract 5 from both sides,

-x = 10 - 5

-x = 5

Multiply the entire equation by (-1)

`\sf \boxed{\bf x = -5}`

y = 5 - 3*(-5)

= 5 + 15

`\sf \boxed{\bf y =20}`