System of Equations

Facts

100

Purpose of Systems of Equations

What is to determine the relationship between two or more equations?

200

No Solution

What is no intersection between both equations

300

Coordinate Solution

What is the point at which both lines intersect?

400

Dependent Solution

What is the solution is the whole line?

500

True or False: System of Equations can be both linear and non-linear?

True

Substitution

100

4x+9y=-19

-4x-7y=13

What is (2,-3)?

200

-5x-3y=14

y=-3

What is (-1,-3)

300

5x + 2y = 21

-x-y = -9

What is (1,8)?

400

-2x+6y = 18

3y = 15

What is (6,5)

500

2x + 3y = -12

-x - 3y = 18

What is (6-,-8)?

Elimination

100

-4x - 2y = -12

4x + 8y = -24

What is (6, -6)

200

x - y = 11

2x + y = 19

What is (10, -1)

300

5x + y = 9

10x- 7y = -18

What is (1,4)?

400

-3x + 7y = -16

-9x + 5y = 16

What is (-4, -4)

500

7x + 2y = 24

8x + 2y = 30

What is (6, -9)

Word Problems

100

Find the value of two numbers if their sum is 12 and their difference is 4.

What is 4 and 8?

200

The difference of two numbers is 3. Their sum is 13. Find the numbers.

What is 5 and 8?

300

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

What is senior citizen ticket: $8, child ticket: $14?

400

The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.

What is Van: 8, Bus: 22?

500

Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?

What is senior citizen ticket: $4, child ticket: $7?