Parallel, Intersecting, or Same Line
Solving by Graphing
Solving by Substitution
Solving Using Elimination
Choosing the Best Method
100
Determine if the graph shows a system of linear equations that is intersecting, parallel, or the same line.
State how many solutions there are for the system.
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 using the substitution method.
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 rewrite the system if it already set up for 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
Elimination
(4,-2)
200
Determine if the graph shows a system of linear equations that is intersecting, parallel, or the same line.
State how many solutions there are for the system.
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 using the substitution method.
y=-4x+1
y=2x+13
(-2,9)
200
Solve each system of equations using the elimination method.
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)
300
Determine if the graph shows a system of linear equations that is intersecting, parallel, or the same line.
State how many solutions there are for the system.
Parallel
No solutions
300
Solve each system of equations by graphing.
y=1/2x-3
y=x-5
(4,-1)
300
Solve the system of equations using the substitution method.
-3x+y=9
y=2x+6
(-3,0)
300
Solve each system of equations using the elimination method.
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)
400
Algebraically determine if the two lines in the system of equations are intersecting, parallel, or the same line.
State how many solutions there will be for the system and explain why.
y=-1/2x-4
y=1/2x+4
Intersecting
One solution
Different slopes
400
Solve each system of equations by graphing.
y=-1/3x
y=1
(-3,1)
400
Solve the system of equations using the substitution method.
x+y=3
x+2y=1
(5,-2)
400
Solve each system of equations using the elimination method.
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
Elimination
(2,1/4)
500
Algebraically determine if the two lines in the system of equations are intersecting, parallel, or the same line.
State how many solutions there will be for the system and explain why.
-6x+3y=12
y=2(x+1)+2
Same line
Infinitely many solutions
Same slopes and same y-intercepts
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
Create and solve the system of equations that represents this situation using the substitution method.
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 and y represent the number of cows Mr. Peters owns.
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.
Create and solve the system of equations to match this situation and solve using the elimination method.
What are the individual costs for a t-shirt and a baseball cap?
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)