Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8. What are the two numbers?

Answer 1

After setting up two equations representing the given conditions, subtracting one equation from the other eliminated one variable, allowing us to find the two mystery numbers: 3 and -5.

Step-by-step explanation:

To solve the system of equations given by the problem, we first set up two equations with our unknowns, which we'll call the first number x and the second number y:

• 6x + 4y = -2 (Equation 1)
• 6x + 2y = 8 (Equation 2)

To eliminate one of the variables, we subtract Equation 2 from Equation 1:

• (6x + 4y) - (6x + 2y) = -2 - 8
• 6x + 4y - 6x - 2y = -10
• 2y = -10

Solving for y, we get:

• y = -10 / 2
• y = -5

Now, we substitute y = -5 into Equation 2 to solve for x:

• 6x + 2(-5) = 8
• 6x - 10 = 8
• 6x = 18
• x = 18 / 6
• x = 3

The two mystery numbers are 3 and -5.