Final answer:
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.