Question

Write a system of linear equations for the problem and solve the system using Gaussian elimination Mike works a total of 57 hr per week at his two jobs. He makes $8 per hour at job A and SO per hour at job B. If his total pay for one week is $474 before taxes, then how many hours does he work at each job?

He works__hr at job A and__hr at job B.

Answer 1

To solve this problem, we can write a system of linear equations using the given information and then use Gaussian elimination to find the solution.

To write a system of linear equations for this problem, we can use the following variables: x for the number of hours worked at job A, and y for the number of hours worked at job B.

We know that the total number of hours worked per week is 57, so we can write the equation:

x + y = 57

Next, we can use the pay rates to create the second equation.

Mike earns $8 per hour at job A, so the amount of money earned from job A is 8x.

Similarly, he earns $5 per hour at job B, so the amount of money earned from job B is 5y.

The total pay for the week is $474, so we can write the equation:

8x + 5y = 474

Now, we can solve this system of linear equations using Gaussian elimination or another method to find the values of x and y.

By solving the system of equations, we find that Mike works 39 hours at job A and 18 hours at job B.