Question

Two times a number minus four times another number is ten, and four times the first number

minus four times the second number results in four. What are the two numbers? Let the first
number be x and the second number bey.

Answer 1

x = -3

y = -4

Explanation:

We're given:

• Two times a number minus four times another number is ten
• Four times the first number minus four times the second number results in four

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

Translate the given information into equations:

• Two times [a number] minus four times [another number] is ten
  
  `2x-4y=10`
• Four times [the first number] minus four times [the second number] results in four
  
  `4x-4y=4`

Now, solve using elimination:

-
`2x-4y=10\\\hspace{5} 4x-4y=4\\\rule{60}{0.3}\\-2x=6`

Solve for x:

`-2x=6\\x=-3`

Therefore, the first number is -3.

Now, solve for y using x:

`2x-4y=10\\2(-3)-4y=10\\-6-4y=10\\-4y=16\\y=-4`

Therefore, the second number is -4.