Transcript Systems of Linear Equations By Dylan Nicoletti Objectives
Systems of Linear Equations
By Dylan Nicoletti Summit High School Adapted from the Traveling Book Seller, Drew Polly, 2006
Objectives
– Using appropriate computation methods 1.2.a
– Use multiple forms of linear equations 2.1.b
– Represent linear functions using a table, graph equations, and convert from one form to another 2.1.c
– Solve equations for one variable in terms of another 2.4.c
– Solve systems of linear equations with two and three variables 2.5.c
Directions
• Use a piece of paper to record all attempts at each problem.
• If you get the wrong answer, look for your mistake and rewrite the problem with your correction so you have a fully written correct response.
• Have fun and remember, you are practicing for a great performance on your upcoming assessment.
Questions
Solving by Graphing Solving by Substitution Solving by Elimination
Credits
All teachers and students at non-profit schools can use, revise, or adapt this game at will at no cost on the condition that all prior designers are cited.
• Adapted from “The Traveling Georgia Artist” by Lloyd Rieber, The University of Georgia, May 20, 2003 • Adapted from “The Traveling Book Seller” by Drew Polly, UNC-Charlotte
That’s Correct!
Sorry, that’s not correct!
1) Graph the system of equations and select the ordered pair that represents the system’s solution.
y
3
x
2
y x
4 2 • ( 2 , 8 ) • ( -2 , 8 ) • ( 2 , -8 ) • ( -2 , -8 )
2)
Two linear equations that have the same slope but different y-intercepts will have the following solution.
• None • One • Infinitely Many • Not Enough Information
3)
By analysis or graphing, the following system has how many solutions?
y
4
x
2
x
2
y
4 8 • None • One • Infinitely Many • Two
4)
If you wanted to graph a system by graphing the equations in slope-intercept form, what would be your first step?
• Solve Each Equation for x • Solve Each Equation for y • Write Equations in Standard • Find the X-Intercept of Each Line
5) Linear equations with different slopes _________ have one solution.
• Never • Sometimes • Always • It depends on the coefficients
6) Solve the following system using substitution.
y
2
x
x y
4 2 • • • • ( 0 , 2 ) ( 2 , 2 ) ( -2 , 0 ) ( 2 , 0 )
7) Solve the following system using substitution.
x
x
2
y
2
y
2 • ( 2 , 0 ) • ( 0 , 2 ) • ( -2 , 0 ) • ( 0 , 0 )
8) Find a and b so that ( 2 , 1 ) is a solution the system.
ax y
by ax
3 2 • a = 1 and b = -4 • a = -1 and b = -4 • a =-1 and b = 4 • No solutions
9)
In the following system, which equation and what variable would you solve for?
4 3
x x
y
7
y
4 3 • Equation 1 for y • Equation 1 for x • Equation 2 for x • Equation 2 for y
10) The total number of points you can earn on a math test is 200 points. Your grade is 85% and you answered 42 problems correctly. Each problem is worth either 3 points or 5 points. How many 5-point problems did you answer correctly?
• 22 • 29 • 30
11) Solve the following system using elimination.
x
y x
y
1 9 • ( 4 , -5 ) • ( 4 , 5 ) • ( 2 , -3 ) • ( -3 , 2 )
12)
Solve the following system using elimination.
5 3
x x
7
y
2
y
2 36 • ( 8 , 2 ) • ( 8 , 4 ) • ( 8 , 6 ) • ( 8 , 8 )
13) Tell whether the system has one solution, no solution , or infinitely many solutions.
3 5
x x
2 4
y y
2 4 • No Solutions • Infinitely Many • One • Sometimes it has none
14)
A store sells recordable compact discs in packs of 5 for $5 and packs of 10 for $8. You but 45 discs for $37. How many of each type of pack did you buy?
• 1 pack of 5; 4 packs of 10 • 8 packs of 5; 1 pack of 10 • 3 packs of 5; 3 packs of 10 • 4 packs of 5; 1 pack of 10
15)
Your school band is performing a concert. Tickets for the concert cost $3 for students and $5 for adults. A total of 125 people attend the concert. Ticket sales total $475. How many students and adults are at the concert.