Number of Solutions
The following system has this many solutions:
y - 13 = 5x
y - 5x = 12
What is "no solution"?
When graphing a system of equations, the solution lies at the point of ______________?
What is "intersection"?
To use the substitution method, what must the format of at least one equation be?
What is "solved for a single variable"?
What is the goal when using the Elimination Method?
What is "to eliminate one variable in each linear equation"?
At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, m, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?
m = 3n + 8
m + n = 54
The following system has this many soltuions:
y = 2x + 10
3y - 6x = 30
What is "infinitely many solutions"?
What does a system of linear equations, with no solution, look like?
What is "parallel lines"?
The solution of the following system of equations:
2y - 2 = 4x
y = -x + 4
What is "(1, 3)"?
Show your work to your group.
The solution of the following system of equations:
3x-6y=3
4x+6y=32
What is "(5, 2)"?
Show your work to your group.
Maricella has a bag containing 35 nickels and quarters. The total value of these coins is less than $2.50. Write a system of linear equations for this situation.
n + q = 35
0.05n + 0.25q = 2.50
The following system has this many solutions:
y - 1/4x = -1
y - 2 = 4x
What is "one solution"?
What do the linear equations, in a system, have in common if their point of intersection is "no solution"?
What is "the same slope"?
The solution of the following system of equations:
y = 5x + 2
2y - 4 = 10x
What is "infinitely many solutions"?
Show your work to your group.
The solution of the following system of equations:
2x+8y=-22
x+5y=-12
What is "(-7, -1)"?
Show your work to your group.
Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?
5f + 3g = 5.70
2f + 10g = 3.60
The following system has this many solutions:
-3x + 1/3y = 12
2y = 18x +72
What is "infinitely many solutions"?
What does a system of linear equations, with infinitely many solutions, look like when graphed?
What is "only one line"?
The solution of the following system of equations:
-3y = -2x -1
y = x - 1
What is "(4, 3)"?
Show your work to your group.
The solution of the following system of equations:
4x + 6y = 40
-2x + y = 4
What is "(1, 6)"?
Show your work to your group.
The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156. Write a system of linear equations to represent this situation.
2s + 3b = 156
s = b + 8 or b = s - 8
The following system has this many solutions:
3y + 6x = 12
8x + 4y = 20
What is "no solution"?
To name the solution of a system of linear equations, with one solution, what would you use?
What is "an ordered pair"?
The solution of the following system of equations:
2y - 2 = 4x
y = -x + 4
What is "no solution"?
Show your work to your group.
The solution of the following system of equations:
-2x + 2y = 2
4x - 4y = 4
What is "no solution"?
Show your work to your group.
A boat can travel 8 miles against the current in 1 hour. The same boat can travel 12 miles with the current in 1 hours. What is the speed of the boat and what is the speed of the current?
b - c = 8
b + c = 12
b = 10 mph
c = 2 mph