queston 15.
Determine the solution to the system of equations below.
-5x – 7y = 11
x – 2y = -9
Responses
A Infinitely many solutionsInfinitely many solutions
B x = -5, y = 2x = -5, y = 2
C No solutionNo solution
D x = -5, y = -7
question 16.
A master electrician earns $62 per hour. His apprentice earns $40 per hour. The master electrician works 3 hours more than the apprentice. If together they are paid $492, how much does the master electrician earn?
Responses
A $292
B $312
C $332
D $372
For question 15, we can solve the system of equations by using the substitution method.
First, solve for x in the second equation:
x = -9 + 2y
Now substitute x into the first equation:
-5(-9 + 2y) - 7y = 11
45 - 10y - 7y = 11
-17y = -34
y = 2
Now substitute y back into x = -9 + 2y:
x = -9 + 2(2)
x = -9 + 4
x = -5
So the solution is x = -5, y = 2, which corresponds to option B.
For question 16, let's represent the number of hours the apprentice works as a, and the number of hours the master electrician works as a + 3.
Now we can create an equation based on their total payment:
40a + 62(a + 3) = 492
40a + 62a + 186 = 492
102a = 306
a = 3
So the apprentice works 3 hours and the master electrician works 6 hours.
Now we can find out how much the master electrician earns:
62 * 6 = $372
Therefore, the master electrician earns $372, which corresponds to option D.