Solve Graphically
Solve Algebraically
Writing Systems of Eqtns
Find the Mistake
Solving Equations
100
Graph the equations y=-1/2x - 5 and x – 2y = 2 on the same set of axes. What is the solution to the system?
(-4,-3)
100
y = -1/2 x - 5
x – 2y = 2 .
Solve the system of equations algebraically. Show your work.
x=-4
y=-3
100
Sean has three blue blocks and six pink blocks that weigh 14 ounces altogether. Ayla has three pink blocks and they weigh the same as two blue blocks. How much does each block weigh?
Write a system of equations that represents this situation.
14=3b+6p
3p=2b
Blue = 2 oz, Pink = 4/3 oz
100
What are the errors (or error) in this solution?
3(x+2) - 2(2x-3) = 13
3x + 6 - 4x +5 = 13
7x +11 =13
7x = 2
x= 2/7
Second line: +5 should be +6;
Third line should be –x + 12 =13, x = –1
100
Solve (x-3)/(x+8) = -2/3. Show all of your steps!
x = –7/5
200
Solve (x-2)2 - 2 = -x + 3 graphically.
200
Solve the system of equations algebraically. Show all of your work and explain how your solution relates to the graph of the system.
2x - y = 5
5x + 2y = 8
x = 2, y = –1, This is the point of intersection of the two lines.
200
Three cans of soda and two bags of chips cost $5.35. Two cans of soda and four bags of chips cost $6.90.
Write a system of equations that represents the situation.
3s+2c=5.35
2s+4c=6.90
A can of soda costs $0.95 and a bag of chips costs $1.25.
200
What are the errors (or error) in this solution? Explain the author’s mistake(s), and then show the correct solution clearly. Write a note to the author explaining how he can avoid making a similar mistake again.
4/(y+2) = -3/(y-2)
-3y + 6 = 4y - 8
-7y = -14
y=2
Second line +6 should be –6
y = 2/7
200
Solve use any method. Check your solution(s).
x=sqrt(2x)+5
x=6 +/- sqrt(11) (- is extraneous)
x=9.317
x=2.683 (extraneous)
300
Graph a system of equations to solve
(x-1)2 + 2 = 3x -1
Show your solutions clearly on your graph.
x = 4 and x = 1
300
Solve (x-2)2 - 2 = -x + 3 algebraically.
x=3.303
x=-0.303
300
Greg works after school in a health food store. He is supposed to add cranberry juice to apple juice to make 20 gallons of cranapple juice. A gallon of the apple juice sells for $3.25 and a gallon of the cranberry juice sells for $4.15. A gallon of the cranapple juice sells for $3.43. How many gallons of each juice should he use in the mixture? Help Greg decide how much of each juice by setting up and solving an equation or system of equations.
c + a = 20
3.25a + 4.15c = 3.43(2)
16 gallons of apple juice and 4 gallons of cranberry
300
Locate and fix the error in the solution:
8(x-3) - 2(x+) = 5(x-1)
8x - 24 -2x + 5 = 5x -5
6x - 19 = 5x - 5
x= 14
2nd line “+5” should be “–6”
x = 25
300
Solve the system of equations without graphing. Explain what the solution tells you about the graph of the system.
y = 1/3 x2 + 1
y = 2x - 2
(3, 4); a line tangent to parabola (touching it at one point)
400
What is the point of intersection for the graphs of these two lines?
5x + y = -7
3x + y = 15
(–11, 48)
400
Solve (x-1)2 + 2 = 3x - 1 algebraically.
Show all your work.
x=4
x=1
400
Write and solve an equation or a system of equations to solve the following problem.
The cost of a hamburger is $1.15 more than an order of large fries. Bill bought two hamburgers and an order of fries for a total of $8.60. What is the price of each item?
h = 1.15 + f
2h + f = 8.60
fries: $2.10, hamburger: $3.25
400
Solve the system of equations without graphing. Explain what the solution tells you about the graph of the system.
y = sqrt(x-3)
y= x - 5
(7, 2); a line intersecting the positive portion of a sleeping parabola, the second algebraic solution, x = 4, is extraneous
500
Solve graphically
6x – 2y = –4
y = 3x + 2
Same line, infinite solutions
500
Solve the system of equations algebraically. Show all of your work leading to the solution and explain how your solution would relate to the graph of the system.
3x - 2y = 6
y = -1/2 x + 4
(7/2, 9/4)
OR
(3.5, 2.25)
500
Write and solve an equation or a system of equations to solve the following problem.
A frozen dinner is five times as expensive as a can of soup. The total price of both items purchased together is $3.12. What is the price for each item?
d = 5s
d + s = 3.12
dinner: $2.60, soup: $0.52
500
Solve the system of equations without graphing. Explain what the solution tells you about the graph of the system.
6x – 2y = –4
y = 3x + 2
infinitely many solutions; lines coincide