Determine whether the system has no, solution, one solution, or infinitely many solutions.
y = -x -2
y = -x - 2
infinitely many solutions, they are the same line
100
Solve using substitution.
y = 2x + 3
y = 4x - 1
(2, 7)
100
Solve using elimination.
2x - 3y = -11
x + 3y = 8
(-1, 3)
100
Write and solve a system of equations to answer the question(s).
The sum of two numbers is 48, and their difference is 24. What are the numbers?
The numbers are 36 and 12.
200
y = -x
y = 2x - 6
(2 , -2)
200
Determine whether the system has no, solution, one solution, or infinitely many solutions.
y = 2x - 2
y = 2x - 5
no solution, the lines are parallel
200
Solve using substitution.
x = 4y + 5
x = 3y - 2
(-23, -7)
200
Solve using elimination.
4x + y = -9
4x + 2y = -10
(-2, -1)
200
Write and solve a system of equations to answer the question(s).
Angles X and Y are supplementary (angles whose sum is 180 degrees). The measure of angle X is 24 degrees greater than the measure of angle Y. Find the angle measures.
Angle X is 102 degrees and Angle Y is 78 degrees.
300
y = 2x + 6
y = -x - 3
(-3, 0)
300
Determine whether the system has no, solution, one solution, or infinitely many solutions.
x + y = 2
y = 4x + 7
one solution, (-1, 3)
300
Solve using substitution.
y = 5x
2x + 3y = 34
(2, 10)
300
Solve using elimination.
-4m + 2n = 6
-4m + n = 8
(-2.5, -2)
300
Write and solve a system of equations to answer the question(s).
Cody bought two pairs of glove and four hats for $43.00. Tori bought two pairs of gloves and two hats for $30.00. What were the prices of the gloves and hats?
Gloves are $8.50 and hats are $6.50.
400
y = -6
y = -4x + 2
(2, -6)
400
Determine whether the system has no, solution, one solution, or infinitely many solutions.
2x + 4y = 2
3x + 6y = 3
Write and solve a system of equations to answer the question(s).
Veronica has been saving dimes and quarters. She has 94 coins in all, and the total value is $19.30. How many dimes and quarters does Veronica have?
She has 28 dimes and 66 quarters.
500
2x + y = -4
5x + 3y = -6
(-6, 8)
500
Determine whether the system has no, solution, one solution, or infinitely many solutions.
2y - 4x = 2
-2x + y = -4
no solution
500
Solve using substitution.
3x + y = 12
y = -x - 2
(7, -9)
500
Solve using elimination.
4x + 7y = 6
6x + 5y = 20
(5, -2)
500
Write and solve a system of equations to answer the question(s).