Question

A first number plus twice a second number is 1. Twice the first number plus the second totals 14. Find the numbers

Answer 1

Hey there!!

Let's take the first number as ' x '

Let's take the second number as ' y '

First number + twice the second number is 1

x + 2y = 1 ------------ ( 1 )

Twice the second number + second number is 14.

2x + y = 14 ----------- ( 2 )

Now let's get them all together...

...................................................................................................................................................................

x + 2y = 1 --- ( 1 )

2x + y = 14 --- ( 2 )

Now, let's multiply the first equation with 2 ...

...................................................................................................................................................................

2x + 4y = 2 --- ( 1 )

2x + y = 14 --- ( 2 )

Now, let's subtract the second equation from the second...

...................................................................................................................................................................

2x + 4y = 2 --- ( 1 )

- ( 2x + y ) = - ( 14 )

...................................................................................................................................................................

2x + 4y = 2 --- ( 1 )

-2x - y = -14 --- ( 2 )

...................................................................................................................................................................

3y = -12

Divide by 3 on both sides...

y = -4

The second number is -4.

We have the first equation x + 2y = 1

We got the y value, now substitute the value of y to get the value of x

...................................................................................................................................................................

x + 2y = 1

x + 2 ( -4 ) = 1

x - 8 = 1

Add 8 on both sides

x = 9

Hence, the second number is 9.

...................................................................................................................................................................

Hope my answer helps!!

Answer 2

Let's consider the first number to be
`f` and the second number to be
`s`. Based on the information in the problem, we can create the following equations:

`f + 2s = 1`

`2f + s = 14`

Now, we can solve the equations through systems of equations. One way of doing this is by multiplying one of the equations so that there is a term in both equations which can be removed by addition or subtraction. In our case, we can multiply the entire first equation by 2 to get:

`2f + 4s = 2/tex]</p><p>[tex]2f + s = 14`

Now, subtract
`2f` from both equations to get:

`3s = -12`

`s = -4`

Now that we have found
`s`, "plug" it back into an equation to find
`f`:

`f + 2(-4) = 1`

`f - 8 = 1`

`f = 9`

Our answers are s = -4 and f = 9.