Let's consider the first number to be [tex]f[/tex] and the second number to be [tex]s[/tex]. Based on the information in the problem, we can create the following equations:
[tex]f + 2s = 1[/tex]
[tex]2f + s = 14[/tex]
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:
[tex]2f + 4s = 2/tex]
[tex]2f + s = 14[/tex]
Now, subtract [tex]2f[/tex] from both equations to get:
[tex]3s = -12[/tex]
[tex]s = -4[/tex]
Now that we have found [tex]s[/tex], "plug" it back into an equation to find [tex]f[/tex]:
[tex]f + 2(-4) = 1[/tex]
[tex]f - 8 = 1[/tex]
[tex]f = 9[/tex]
Our answers are s = -4 and f = 9.
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.
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Hope my answer helps!!
