Graphing Systems of Equations
Intersect. (x, y).
Which inequality symbol would be in an equation with a dashed line, shaded above?
>
Solve using the substitution method. Your answer must be in the correct form.
y = 0
y = x + 2
(-2, 0)
Solve using the elimination method. Your answer must be in the correct form.
x + 2y = 4
-x + 4y = 8
(0, 2)
Express the situation given in this word problem as an equation:
I bought tacos and chips for lunch. Tacos are $3 each, and drinks are $2 each. I spent $20 on lunch. Let x represent the number of tacos I bought, and let y represent the number of drinks I bought.
3x + 2y = 20
The solution set of two lines is ___________ if the two lines have the same m & b. The solution set is ___________ if the two lines have the same m and different b's.
Infinite solutions, No solution
Which quadrant of the coordinate plane would the answer to this system of inequalities lie in?
x > 0
y > 0
(Q1 = top right, Q2 = top left, Q3 = bottom left, Q4 = bottom right)
Q1
Solve using the substitution method. Your answer must be in the correct form.
y = -x - 3
y = x + 1
(-2, -1)
Solve using the elimination method. Your answer must be in the correct form.
x - 2y = 5
x + 2y = 1
(3, -1)
I bought tacos and chips for lunch. Tacos are $3 each, and drinks are $2 each. I spent $20 on lunch. Let x represent the number of tacos I bought, and let y represent the number of drinks I bought.
Is it possible for me to have ordered 3 tacos? If so, how many drinks did I order?
No, it's not possible.
The equation is 3x + 2y = 20.
If x = 3, then y = 5.5. It's impossible to order a half a drink, because I can only order in whole numbers.
Solve this system by graphing. Your answer must be in correct form.
y = 2
y = x + 2
(0, 2)
Which quadrant of the coordinate plane would the MAJORITY of the answers to this system of inequalities lie in?
y > x - 1
x < 0
(Q1 = top right, Q2 = top left, Q3 = bottom left, Q4 = bottom right)
Q2
Solve using the substitution method. Your answer must be in the correct form.
y = -x + 1
y = x + 2
(-0.5, 1.5)
Solve using the elimination method. Your answer must be in the correct form.
2x + 3y = 10
-x + 2y = 9
(-1, 4)
Solve the system of equations. Write your answer as (x, y).
The Game Store sells cards and board games. Lisa bought 5 packs of cards and 12 board games, spending $70. John bought 10 packs of cards and 4 board games, spending $40. What is the price of cards, x, and what is the price of board games, y, at The Game Store? Write your answer as (x, y).
(2, 5)
Solve this system by graphing. Your answer must be in correct form.
y = x - 1
y = -1/2 x + 2
(2, 1)
Which quadrant of the coordinate plane would the answers to this system of inequalities lie in?
x < 0
y < 0
y > 5x - 1
(Q1 = top right, Q2 = top left, Q3 = bottom left, Q4 = bottom right)
Q3
Solve using the substitution method. Your answer must be in the correct form.
2x - 2y = -6
y = 1/2 x + 3
(0, 3)
Solve using the elimination method. Your answer must be in the correct form.
y + 7 = 8x
-3y - 10 = -2x
(0.5, -3)
Express the situation given in this word problem as a system of inequalities:
Sam has $50 to spend on clothes, but he doesn't want to spend all of it. He needs to come home with one outfit (a shirt and pants) no matter what. He can buy shirts for $10 each, or pants for $14 each. Let x represent the number of shirts he can buy, and let y represent the number of pants he can buy.
10x + 14y < 50
x > or equal to 1
y > or equal to 1
Solve this system by graphing. Your answer must be in correct form.
6x - 3y = 3
2x - 1 = y
No solution or {}
Which quadrant of the coordinate plane would the MAJORITY of the answers to this system of inequalities lie in?
y > -2
x < 3
y > 2x -1
(Q1 = top right, Q2 = top left, Q3 = bottom left, Q4 = bottom right)
Q2
Solve using the substitution method. Your answer must be in the correct form.
x - y = 3.5
3x - 6.5y = 3.5
(5.5, 2)
Solve using the elimination method. Your answer must be in the correct form.
3x = -4y - 7
5y - 20 = 2x
(-5, 2)
Answer each part of the questions below as yes or no.
Sam has $50 to spend on clothes. He can spend all of it, if he wishes. He can buy shirts for $9 each, or pants for $12 each. Let x represent the number of shirts he can buy, and let y represent the number of pants he can buy.
1. Is (0 , 0) a solution to the system?
2. Is (5, 0) a solution to the system?
3. Is (-2 , 5) a solution to the system?
4. Is it possible for Sam to spend all of his money on clothes?
1. Yes
2. Yes
3. No
4. No