Question

Twice one number added to another
number is 18. If the second number is equal
to 12 less than 4 times the first number, find
the two numbers.
First complete the equations below, where x stands for
the first number and y stands for the second number.
2x + y = 18; y = [?]x-[]

Answer 1

Answer:

The Answer is: The first number is 5 and the second one is 8.

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Step-by-step explanation:

Let f = first number and s = second number

Twice the first number added to the second number is 18:

2f + s = 18

The second number is equal to 4 times the first number minus 12:

s = 4f - 12

Substitute:

2f + (4f - 12) = 18

6f - 12 = 18

6f = 18 + 12

6f = 30

f = 5, is the first number.

Solve for the 2nd number:

s = 4(5) - 12 = 20 - 12 = 8, is the second number.

Proof:

2f + s = 18

2(5) + 8 = 18

18 = 18

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Answer 2

Answer:

y = 8

x = 5

Step-by-step explanation:

This is a system of equations problem

Set up your two conditions:

2x + y = 18

y = 4x - 12

rearrange them to match

y = -2x + 18

y =   4x - 12

combine them by subtracting one equation from the other in such a way that it eliminates one variable. In this case I choose to subtract each value from the second equation from the first one

0 = -6x + 30

solve

6x = 30

x = 5

plug in the x value to solve for y

2(5) + y = 18

10 + y = 18

y = 8