Distributive Property
Create the Equations
Substitution
Slope
Grab Bag
100
Solve for x.
6(−5x + 7) = -18
x = 2
100
Josh decides to team up with Nick Mercs to play Warzone. Due to a glitch in the game, Josh starts with 250 damage. Josh inflicts 600 damage every game, and Nick inflicts 650 damage. What is the system of equations for both players?
Josh: y = 600x + 250
Nick: y = 650x
100
Solve the systems of equations using substitution.
x = 5
x + y = 12
(5, 7)
100
The equation for calculating the slope between two points.
m = (y2 - y1) / (x2 - x1)
100
Does the following equation have one solution, no solution, or infinitely many solutions?
3x - 6 = -3x - 6
One solution, x = 0
200
Solve for x.
4(3x - 1) - 5 = 75
x = 7
200
Ahmose hits up Steph Curry to do a stair workout. Ahmose starts on the ground floor, and Steph begins five floors under him. It takes Ahmose 50 seconds to climb one flight of stairs and Steph 40 seconds. What system of equations describes their ascent?
Ahmose: y = 50x
Steph: y = 40x - 5
200
Solve the systems of equations using substitution.
y = 2x
x + y = 9
(3, 6)
200
What is the slope of the line on the graph?
m = 1/1
200
Rewrite the following equation in slope-intercept form:
9x + 3y = 36
y = -3x + 12
300
Solve for x.
6x - 2(x - 5) =46
x = 9
300
McKenzie and Vanessa met up and watched tv together. They watched a 90 minute show, but McKenzie had to leave after 70 minutes of it. At home, McKenzie watches two episodes of a 30 minute show every night. Vanessa also watches a show every night, that's one hour long. What system of equations describes their tv watching habits?
McKenzie: y = 60x + 70
Vanessa: y = 60x + 90
300
Solve the systems of equations using substitution.
y = -3x
4x - 2y = -20
(-2, 6)
300
What is the slope of the line created by these data points?
4/1
300
Which of the following lines has the greatest rate of change (i.e., the steepest line)?
y = 10x
y = 1/2x + 7
y = 5/2x + 10
y = 10x
400
Solve for y.
3(y - 1) + 2(y +3) = 13
y = 2
400
Mr. Falotico's socks have a mysterious way of disappearing. Apparently Mr. Corrinet has the same issue. Mr. Falotico has 45 PAIRS of socks, and he loses one pair a month -- while Mr. Corrinet has 40 PAIRS and loses two pairs a month. What system of equations describes their TOTAL sock situation?
Mr. Falotico: y = -2x + 90
Mr. Corrinet: y = -4x + 80
400
Solve the systems of equations using substitution.
x = 3yx - 3y = 0
Infinitely many solutions
400
Are the following points on the same line?
(0,0)
(2.5, 8)
(4, 16)
No
400
Create two equations that will share a solution at (0,42)
Answers will vary, should both share 42 as y-intercept.
Ex: y = -3x + 42 & y = x + 42
500
Solve for x.
4(x + 12) = 2(2x + 8) + 10No solution
500
Currently there are 50 Republicans in the US Senate, and 50 Democrats+Independents. Joe Biden and Kamala Harris seek to pass a major covid-inspired infrastructure bill. Biden talks with the Democrats/Independents. He knows 40 of them currently support the bill, but each week three change their mind and decide to vote against it. Kamala talks with the Republicans. Initially, 6 are supportive, but each week two flip and decide to vote for it. What system of equations describes support for the infrastructure bill?
Biden (Ds/Is): y = -3x + 40
Harris (Rs): y = 2x + 6
Bonus: What equation describes the Senate's overall support for the bill? There are 100 senators in total.
500
Solve the systems of equations using substitution.
y = 2x
-6x + 3y = 16
No solution
500
What is the slope of the line on the graph?
2/3
500
The girls' volleyball team is selling holiday cards and tree ornaments to raise money for new equipment. For each holiday card they make $5, and for each tree ornament they make $9. If they need to raise $200 in total, what is one combination of the number of holiday cards and tree ornaments they need to sell?
4 Holiday Cards
20 Tree ornaments
(May accept other solutions)