Number of Solutions
Solving Systems by Graphing
Solving Systems Using Tables
Solving Systems by Substitution
Solving Systems Using Linear Combination/Elimination
Choosing the Best Method for Solving Systems
Applications (Story Problems) of Systems of Equations
BONUS: Repeating Decimals to Fractions
100
Intersecting, Parallel, or Same Line?
AND
How many solutions?
Intersecting
One solution
100
Decide whether the given ordered pair is a solution of the system of equations.
y=2x-1
y=1/3x+4
(3,5)
Yes
100
Solve the system of equations (done best by INPUT-OUTPUT TABLES, both in Slope-Intercept Form with integer R.o.C./Slopes).
(1,1)
100
Solve the system of equations (done best by SUBSTITUTION, x is isolated in equation #1).
x=y+1
3x+2y=18
(4,3)
100
Transform the system of linear equations into a system that is ready for columns to be added together to eliminate a variable OR simply rewrite the system if it already set up for LINEAR COMBINATION/ELIMINATION.
3x-y=3
6x+2y=9
6x-2y=6
6x+2y=9
100
State the best method to solve the system of linear equations and then solve.
2x+y=6
x-y=6
Linear Combination/Elimination
(4,-2)
100
Answer the question by setting up and solving a system of equations.
Two jet ski rental companies have different costs.
Company A charges a flat fee of $8 plus $2.50 per hour.
Company B charges a flat fee of $14 plus $1.00 per hour.
At what point in time are both rentals the same amount AND how much are the rentals for that amount of time?
y=2.5x+8
y=x+14
(4,18)
After 4 hours the rentals cost the same amount of $18.
100
*The trick:
1. Figure out how many digits are repeating.
2. Put the repeated portion over the largest multiple of 9 with the same number of digits as the repeated portion.
i.e. Decimal = 0.272727... -> Repeated Portion = 27 (2 digits) -> 27/99 (each 2 digits) = 3/11 (reduced)
Convert the repeating decimal into a fraction.
0.555...
5/9
200
Intersecting, Parallel, or Same Line?
AND
How many solutions?
Same line
Infinitely many solutions
200
Decide whether the given ordered pair is a solution of the system of equations.
y=x-2
4x+y=-2
(0,-2)
Yes
200
Solve the system of equations (done best by INPUT-OUTPUT TABLES, both in Slope-Intercept Form with integer R.o.C./Slopes).
(-4,-9)
200
Solve the system of equations (done best by SUBSTITUTION, y is isolated in both equations).
y=-4x+1
y=2x+13
(-2,9)
200
Solve the system of equations (done best by LINEAR COMBINATION/ELIMINATION, both equations in Standard Form).
x+3y=17
2x-3y=-20
(-1,6)
200
State the best method to solve the system of linear equations and then solve.
x=y-1
3x+y=13
Substitution
(3,4)
200
Answer the question by setting up and solving a system of equations.
The Mendenhall Theater sells two types of tickets: youth and adult. The theater holds a total of 450 people.
One night, the theater sold all their tickets for total of $2,706. Youth tickets cost $4.60 and adult tickets cost $7.00.
How many tickets of each type did the theater sell that night?
x+y=450
4.6x+7y=2,706
(185,265)
The theater sold 185 youth tickets and 265 adult tickets.
200
*The trick:
1. Figure out how many digits are repeating.
2. Put the repeated portion over the largest multiple of 9 with the same number of digits as the repeated portion.
i.e. Decimal = 0.272727... -> Repeated Portion = 27 (2 digits) -> 27/99 (each 2 digits) = 3/11 (reduced)
Convert the repeating decimal into a fraction.
0.818181...
9/11
300
Intersecting, Parallel, or Same Line?
AND
How many solutions?
Parallel
No solutions
300
Solve the system of equations (done best by GRAPHING, both in Slope-Intercept Form with fractional R.o.C./Slopes).
y=1/2x-3
y=x-5
(4,-1)
300
Solve the system of equations (done best by INPUT-OUTPUT TABLES, both in Slope-Intercept Form with integer R.o.C./Slopes).
y=x+2
y=2x-1
(3,5)
300
Solve the system of equations (done best by SUBSTITUTION, y is isolated in equation #2).
-3x+y=9
y=2x+6
(-3,0)
300
Solve the system of equations (done best by LINEAR COMBINATION/ELIMINATION, both equations in Standard Form).
5x+4y=22
2x+4y=16
(2,3)
300
State the best method to solve the system of linear equations and then solve.
y=1/3x-5
y=-4/3x
Graphing
(3,-4)
300
Answer the question by setting up and solving a system of equations.
Jamal and Emily each started a savings account in January.
Jamal started with $46 in his account and added $24 each month.
Emily opened her account with $319. Each month she withdrew $15.
After how many months will they have the exact same amount in their accounts AND how much will be in their accounts at that time?
y=24x+46
y=-15x+319
(7,214)
After 7 months they will both have $214 in their accounts.
300
*The trick:
1. Figure out how many digits are repeating.
2. Put the repeated portion over the largest multiple of 9 with the same number of digits as the repeated portion.
i.e. Decimal = 0.272727... -> Repeated Portion = 27 (2 digits) -> 27/99 (each 2 digits) = 3/11 (reduced)
Convert the repeating decimal into a fraction.
0.232323...
23/99
400
Intersecting, Parallel, or Same Line? Explain why.
AND
How many solutions?
y=-1/2x-4
y=1/2x+4
Intersecting
Different slopes
One solution
400
Solve the system of equations (done best by GRAPHING, both in Slope-Intercept Form with fractional R.o.C./Slopes).
y=-1/3x
y=1
(-3,1)
400
Solve the system of equations using INPUT-OUTPUT TABLES (solve for y in equation #1, then use tables).
2x-y=-13
y=11+x
(-2,9)
400
Solve the system of equations (done best by SUBSTITUTION, either variable is easy to isolate in equation #1).
x+y=3
x+2y=1
(5,-2)
400
Solve the system of equations (done best by LINEAR COMBINATION/ELIMINATION, both equations in Standard Form).
2x+y=7
4x-3y=-6
(1.5,4)
400
State the best method to solve the system of linear equations and then solve.
3x+4y=7
x-8y=0
Linear Combination/Elimination
(2,1/4)
400
Answer the question by setting up and solving a system of equations.
Two girls sold lemonade together. The entire lemonade sale brought in $28.
One girl made $4 more than twice the amount the second girl made.
How much did each girl make at the lemonade sale?
x+y=28
x=2y+4
(20,8)
One girl made $20 while the other made $8.
400
*Ignore the whole number until the end, then put it back in front of your fraction
i.e. Decimal = 4.272727... -> Ignore the 4 -> Repeated Portion = 27 -> 27/99 = 3/11 -> Put back the 4 ->
4 3/11
Convert the repeating decimal into a fraction.
2.666...
2 2/3 or 8/3
500
Intersecting, Parallel, or Same Line? Explain why.
AND
How many solutions?
-6x+3y=12
y=2(x+1)+2
Same line
Same slopes and same y-intercepts
Infinitely many solutions
500
Sandra and Terry each walk to the same school from different neighborhoods. They do not cross paths until they reach the school building. Sandra follows the path represented by the equation
y=-2x+10
and Terry follows the path represented by the equation
y=-1/6x-1
What are the coordinates of the school building?
(6,-2)
500
Solve the system of equations using INPUT-OUTPUT TABLES (find the rate of change between intercepts in each table, then work through tables to find the solution).
2x+3y=20
-x+2y=4
(4,4)
500
Both of Monique's neighbors owned cows.
Mr. James owned five less than three times the number of cows owned by Mr. Peters.
The total number of cows owned by both neighbors was 79.
How many cows did each neighbor own?
Let x represent the number of cows Mr. James owns.
Let y represent the number of cows Mr. Peters owns.
Create and solve the system of equations that represents this situation (done best by SUBSTITUTION, x will be isolated in equation #1).
x=3y-5
x+y=79
(58,21)
Mr. James = 58 cows
Mr. Peters = 21 cows
500
Patrick bought one baseball cap and one t-shirt for $36.
Sammy bought two baseball caps identical to Patrick's caps along with three of the same t-shirts. Sammy spent a total of $94.
What are the individual costs for a t-shirt and a baseball cap?
Create and solve the system of equations to match this situation (done best by LINEAR COMBINATION/ELIMINATION, both equations will be in Standard Form).
x+y=36
2x+3y=94
(14,22)
Baseball Cap = $14
T-shirt = $22
500
State the best method to solve the system of linear equations and then solve.
y=1/2x+3
-3x+4y=18
Substitution
(-6,0)
500
GOOD JOB ON FINDING THE ONE FREEBIE!
BONUS 500 POINTS!
500
*Ignore the whole number until the end, then put it back in front of your fraction
i.e. Decimal = 4.272727... -> Ignore the 4 -> Repeated Portion = 27 -> 27/99 = 3/11 -> Put back the 4 ->
4 3/11
Convert the repeating decimal into a fraction.
1.330330330...
1 110/333 or 443/333