Systems of 2 Equations
The solution to the system:
-8x + 7y = -2
8x - 8y = -8
What is the point (9, 10)?
Theresa went back to school shopping with her three children. The first child needed three notebooks, four pencils and two pens for a total of $5.45. The second child needed five notebooks, two pencils, and three pens totaling $7.80. Her last child needed two notebooks, five pencils and four pens for a total cost of $5.15. Find the cost of each item.
$1.25 per notebook, $0.25 per pencil and $0.35 per pen.
The graph of the solution to the system:
y ≤ x + 7
y ≤ -2x - 5
See my graph.
The solution to the system:
9x + 2y = 49
-3x +5y = -5
What is the point (5, 2)?
A football team scored a total of 50 points in one game. They scored 14 times. The scoring was made up of touchdowns (6 points each), PATs (1 point each), and field goals (3 points each). They had three more touchdowns than field goals. How many of each type of score did the team have?
The team scored 6 touchdowns, 5 PATs, and 3 field goals.
The graph of the solution to the system:
y < x - 6
y < -3/2 x - 1
See my graph.
The solution to the system:
2x + 2y = -10
6x + 8y = -48
What is the point (4, -9)?
A movie theater is filled to capacity of 350. The theater charges $4.50 for children, $7.50 for students, and $12.50 for adults. There are half as many adults as there are students. If the total ticket sales was $2415, how many children, students and adults attended?
170 children, 120 students and 60 adults attended.
The graph of the solution to the system:
-5x + 4y ≤ -20
y < -1/2x + 2
See my graph.
The solution to the system:
4x + 6y = 16
-7x +2y = -3
What is the point (1, 2)?
Mike is taking a math test and has 2 hours (120 minutes) to complete it. It takes him 5 minutes to complete a multiple choice question, 5 minutes to complete a calculation question, and 10 minutes to complete a word problem. He must complete 20 questions total. The number of multiple choice questions on the test is equal to the number of calculation questions and word problems combined. If Mike is able to finish on time, how many of each type of question was there?
There were 10 multiple choice questions, 6 calculation problems, and 4 word problems.
The graph of the solution to the system:
-x + y ≥ 4
x + 3y > -12
See my graph.
The solution to the system:
4x - 5y = -6
-6x + 7y = 12
What is the point (-9, -6)?
The perimeter of a triangle is 53 cm. The shortest side is half the length of the longest side and the longest side is 2 cm less than twice the middle length side. What is the length of each side?
The shortest side is 13 cm, the medium length side is 14 cm and the longest side is 26 cm.
The graph of the solution to the system:
x ≤ -3
-5x - 3y < 9
See my graph.