Solve the system by graphing.
y = 2/3 x - 3
y = -2x + 5
What is (3, -1)?
100
Solve this system of equations by substitution:
y = 2x - 4
7x - 2y = 5
What is (-1, -6)?
100
Solve this system of equations by elimination:
x + 3y = -2
x - 3y = 16
What is (7, -3)?
100
Determine whether this system has one solution, no solutions, or infinite solutions and explain why.
y = 2x - 2
y = 2x + 9
What is no solution because the slope is the same so the lines are parallel and will never intersect.
100
You have a total of 5 quarters and dimes in your pocket. The value of the coins is $0.80. Write and solve a system of linear equations to find the number x of dimes and the number y of quarters in your pocket.
What is 3 dimes and 2 quarters?
200
Solve this system by graphing:
y = 2x + 5
y = -4x - 1
What is (-1, 3)?
200
Solve this system of equations by substitution:
y = 2x + 3
y = 5x
What is (1, 5)?
200
Solve this system of equations by elimination:
2x - y = 9
4x + y = 21
What is (5, 1)?
200
Determine whether this system of equations has one solution, no solutions, or infinite solutions and explain why.
y = 8x - 2
y - 8x = -2
What is infinite solutions, they have the same equation, so they are the same line.
200
A gift basket that contains jars of jam and packages of bread mix costs $45. There are 8 items in the basket. Jars of jam cost $6 each, and packages of bread mix cost $5 each. Write and solve a system of linear equations to find the number of jars of jam and the number of packages of bread mix.
What is 3 jars of jam and 5 packages of bread mix?
300
Solve this system by graphing:
y = x - 1
y = -x + 3
What is (2, 1)?
300
Solve this system of equations by substitution:
y = x - 4
y = 4x - 10
What is (2, -2)?
300
Solve this system of equations by elimination:
4x + 3y = -5
-x + 3y = -10
What is (-5, -5)?
300
Determine whether the system has one solution, no solutions, or infinite solutions, and explain why.
2y = 6x + 4
y - 3x = 5
What is no solution, the slopes are the same so the lines are parallel and they don't intersect.
300
The length of a sand volleyball court is twice its width. The perimeter is 180 feet. Find the length and width of the court.
What is length is 60 feet and width is 30 feet?
400
Solve this system of equations by graphing:
y = x
y = 2x + 1
What is (-1, -1)?
400
Solve this system of equations by substitution:
y = 2x + 5
y = 3x - 1
What is (6, 17)?
400
Solve this system of equations by elimination:
2x - y = 0
3x - 2y = -3
What is (3, 6)?
400
Determine whether this system of equations has one solution, no solution, or infinite solutions and explain why.
1/3x + y = 1
2x + 6y = 6
What is infinite solutions, they are the same line.
400
The sum of two numbers is 38. The greater number is 8 more than the other number. Find each number.
What is 15 and 23?
500
Solve this system of equations by graphing:
y = 2x + 9
y = 6 - x
What is (-1, 7)?
500
Solve this system of equations by substitution:
y - x = 0
2x - 5y = 9
What is (-3, -3)?
500
Solve this system of equations by elimination:
-2x + 3y = 7
5x + 8y = -2
What is (-2, 1)?
500
Determine whether the system of equations has one solution, no solutions, or infinite solutions and explain why.
y = 3x + 1
-x + 2y = -3
What is one solution, the slopes are not the same.
500
Members of a movie rental club pay a $15 annual membership fee and $2 for new release movies. Nonmembers pay $3 for new release movies. When is it beneficial to have a membership?