System of Equations (general and graphing)
Tell whether the ordered pair is a solution of the system of linear equations.
(8,2)
x-y=6
2x-10y=4
Not a Solution
Solve the equation for y
x-2y=0
y=1/2
Solve the system of linear equations by elimination
9x+y=2
-4x-y=-17
(-3,29)
Determine whether the system has one solution, no solution, or infinitely many solutions
-x+y=1
x-y=1
No Solution
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. Which equations represents the system that could be used?
3s + 1c = 38
3s + 2c = 52
Tell whether the ordered pair is a solution of the system of linear equations.
(-4,-2)
y=2x+6
y=-3x-14
Is a solution
Solve the equation for y
3x+5y=25
y=-3/5x+5
Solve the system of linear equations by elimination
-x+y=4
x+3y=4
(-2,2)
Determine whether the system has one solution, no solution, or infinitely many solutions
2x-2y=4
-x+y=-2
Infinitely Many Solutions
Last season two running backs on the Steelers football team rushed a combined (both running backs) total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?
x + y = 1550
y = 4x
Solve the system of linear equations by graphing
y=-x+4
y=2x-8
(4,0)
Solve the system of linear equations by substitution.
6x-9=y
y=-3x
(1,-3)
Solve the system of linear equations by elimination
10x-9y=46
-2x+3y=10
(19,16)
Solve the system of linear equations.
y=-6x-8
y=-6x+8
No Solution
On Monday Joe bought 10 cups of Coffee and 5 Doughnuts for his office at the (total) cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of Coffee and 10 Doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?
10c + 5d = 16.50
5c + 10d = 14.25
Solve the system of linear equations by graphing
4x-4y=3
y=-5
(0,-5)
Solve the system of linear equations by substitution.
-5x+3y=51
y=10x-8
(3,22)
Solve the system of linear equations by elimination
-2x-5y=9
3x+11y=4
(-17,5)
Solve the system of linear equations.
15x-5y=-20
-3x+y=4
Infinitely Many Solutions
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, t, 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?
t + n = 54
t = 3n + 8
Solve the system of linear equations by graphing
3y+4x=3
x+3y=-6
(3,-3)
Solve the system of linear equations by substitution.
2x-y=23
x-9=-1
(8,-7)
Solve the system of linear equations by elimination
12x-7y=-2
8x+11y=30
(1,2)
Solve the system of linear equations.
3x-2y=-5
4x+5y=47
(3,7)
Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out (all) the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels? (Hint: How much are the coins worth?)
d + n = 80
.10d + .05n = 6.60