Question

1. What is the solution to the following system of equations?

2x + 3y = 6
x + y = 4

The solution of the system of equations is (___, ___).
2. Given the system of equations:

2x – y = –2
x = 14 + 2y

What is the value of the system determinant?
What is the value of the y−determinant?
What is the value of the x−determinant?
What is the solution to the system of equations?
3. Choose the equation and the inequality needed to answer this question. (SELECT ALL THAT ARE CORRECT!!!)

Trevor tutors French for $15 and hour and scoops ice cream for $10 an hour. He is going to work 15 hours this week. At least how many hours does he need to tutor to make more than $180? Let x equal the number of hours he tutors and y be the number of hours he scoops ice cream.

x + y = 15
x + y > 15
x + y < 15
15x + 10y = 180
15x + 10y > 180
15x + 10y < 180
4. Trevor tutors French for $15 and hour and scoops ice cream for $10 an hour. He is going to work 15 hours this week. How many hours does Trevor need to tutor to make at least $180?

_____ hours

Answer 1

1.
2x + 3y = 6
x + y = 4
Solving
x = 6
y = -2

2. 2x- y = -2
x - 2y = 14
Solving
x = 18/-3 = -6
y = 30/-3 = -10

D system = | 2  -1 | = -3
                   | 1  -2 |

D y = | 2  -2 | = 30
         | 1  14 |

D x = | -2  -1 | = 18
         | 14  -2 |

3.
Let x equal the number of hours he tutors and y be the number of hours he scoops ice cream

He is going to work 15 hours so 
x + y = 15
more than $180 so
15x + 10y > 180

4.
solving the above, y = 15 - x
substituting
15x + 10(15-x) > 180
15x +150 - 10x > 180
5x > 30
x > 6

Answer 2

Hey there,

2x + 3y = 6

x = 6

y = -2

This would include that your correct answer would be -2

Hope this helps!