Introduction to Systems of Equations

Name:

Class:

Date:

Show your work for each problem.

1.
What is a system of equations?
1. a)A graph with multiple lines
2. b)Two or more equations with the same variables
3. c)One equation with one variable
4. d)An expression with multiple terms
2.
What does the solution to a system of equations represent graphically?
1. a)The intersection point of the lines
2. b)The y-intercept of both lines
3. c)The slope of the lines
4. d)The distance between the lines
3.
Is a solution to the system: and ?
1. a)Yes, it satisfies both equations
2. b)No, it satisfies neither equation
3. c)No, it only satisfies the second equation
4. d)No, it only satisfies the first equation
4.
If and , what is the value of ?
5.
If and , what is the value of ?
6.
What happens when two lines are parallel?
1. a)The system has no solution
2. b)The system has infinitely many solutions
3. c)The system has exactly one solution
4. d)The system cannot be determined
7.
Verify if is a solution to: and
8.
The lines and intersect at a point. What is the -coordinate of that point?
9.
The lines and intersect at a point. What is the -coordinate of that point?
10.
Find the solution to: and
11.
At a store, 3 pencils and 2 erasers cost 8 euros. 1 pencil and 4 erasers cost 6 euros. Find the price of one pencil.
12.
Which system has infinitely many solutions?
1. a) and
2. b) and
3. c) and
4. d) and
13.
The sum of two numbers is 15 and their difference is 3. What is the larger number?
14.
A parking lot has cars and motorcycles. There are 50 vehicles in total and 160 wheels. How many cars are there?
15.
Find where the lines and intersect.
16.
Movie tickets cost different amounts for adults and children. 2 adult tickets and 3 child tickets cost 36 euros. 3 adult tickets and 2 child tickets cost 39 euros. What is the price of one adult ticket in euros?