Question

The sum of two numbers is 36. Twice the first number minus the second is 6. Find the numbers. (Let the sum of the equations represent line 1 and the difference of the equations represent line 2.)

What is equation #1?

What is equation #2?

What is the solution to the set of equations?

Answer 1

The first equation (Equation #1) is x + y = 36 and the second equation (Equation #2) is 2x - y = 6. The solution to the system is x = 14 and y = 22, which can be found by using the elimination method.

Step-by-step explanation:

We are provided with a system of two linear equations based on the given word problem. Let's define the first number as x and the second number as y.

Equation #1

The sum of the two numbers is 36, so our first equation is:

x + y = 36

Equation #2

Twice the first number minus the second is 6, which gives us our second equation:

2x - y = 6

Solution to the Set of Equations

To solve for x and y, we can use substitution or elimination. Let's use the elimination method:

Add both equations to eliminate y:

3x = 42

Divide by 3 to find x:

x = 14

Substitute x=14 into Equation #1 to find y:

y = 22

The solution to the system of equations is x = 14 and y = 22.