Question

The sum of two numbers is 73. The difference of two times the first number and three times the second number is 1. Find the two numbers. Let x represent the first number, and y represent the second number.

System:
a. x + y = 73, 2x - 3y = 1
b. x - y = 73, 2x + 3y = 1
c. x + y = 73, 3x - 2y = 1
d. x - y = 73, 3x + 2y = 1

Answer 1

The correct system of equations for the problem is a. x + y = 73, 2x - 3y = 1. By using substitution or elimination, we can find the two numbers, which are 44 and 29.

Step-by-step explanation:

The correct system of equations to represent the given problem is a. x + y = 73, 2x - 3y = 1. To solve this system, we can use the method of substitution or elimination. Let's use substitution as follows:

• Solve the first equation for y: y = 73 - x.
• Substitute y into the second equation: 2x - 3(73 - x) = 1.
• Simplify and solve for x: 2x - 219 + 3x = 1 giving us 5x = 220, so x = 44.
• Now substitute x back into the equation for y: y = 73 - 44, which gives us y = 29.

Therefore, the two numbers are 44 and 29.