system of equations

Question

The sum of two numbers is 16. two more than the first number plus three times the second number equals 18. find the numbers.

Answer 1

Let's let x represent the first number and y represent the second number. Then since the sum of the two numbers is 16, we can write the following:

x + y = 16

Next, we can replace the text, "two more than the first number plus three times the second number equals 18" with the following:

x + 2 + 3y = 18

This is equivalent to x + 3y = 16 after subtracting 2 from both sides of the equation.

Now we can use our two equations with two unknowns and solve for x and y (using substitution).

Using our first equation, we can write x = 16 - y and substitute this expression for x into the second equation:

x + 3y = 16

16 - y + 3y = 16

Combine like terms and subtract 16 from both sides of the equation::

16 +2y =16

16 + 2y -16 = 16 -16

2y = 0

y=0

Then if y is 0, then x is 16.

To verify, using the first number as 16 and the second as 0:

16 + 0 =16

AND

2 + 16 + 3* 0 =18