Parallel, Intersecting, or Same Line
Verifying Solutions / Solving by Graphing
Solving by Substitution
Solving Using Elimination
Choose Your 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 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
Choose a method to solve the system of linear equations and then solve.
2x+y=6
x-y=6
(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
Choose a method to solve the system of linear equations and then solve.
x-y=-1
3x+y=13
(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+5=x
(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
Choose a method to solve the system of linear equations and then solve.
y=1/3x-5
y=-4/3x
(3,-4)
400
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.
y=2x-4
y=2x+4
Parallel
No solution
400
Solve each system of equations by graphing.
y+1/3x=0
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
Choose a method to solve the system of linear equations and then solve.
3x+4y=7
x-8y=0
(2,1/4)
500
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.
y=2x+2
2y=4x+4
Same line
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
Choose a method to solve the system of linear equations and then solve.
y=1/2x+3
-3x+4y=18
(-6,0)