Solving Systems by Graphing
Solving Systems by Substitution
Solving Systems by Elimination
Graphing Linear Inequalities
100
How many solutions?
None
100
What would the system look like after the first step of the substitution method is used?
y + x = 1
x = 1 + y
y + (1 + y) = 1
100
Show a first step using the elimination method.
y = 2x +5
y = x + 4
y = 2x + 5
y = x + 4
________
0 = x + 1
100
When graphing a linear inequality, when would you use a dotted line?
When the inequality is just less than or greater than.
200
How many solutions?
Infinitely many
200
Show the next step after the first substitution is completed:
y = 2x - 1
x + y = 1
x + (2x - 1) = 1
200
Show a first step in using the elimination method.
2y = 2x - 4
y = 3x - 2
Multiply the second equation by 2.
y = 3x - 2 ==> 2y = 6x - 4
200
What is the equation of this linear inequality?
y > 2x +1
300
What is the solution?
(2,2)
300
Solve using substitution. Show your work!
y = x + 1
x + y = 1
x + (x + 1) = 1
2x + 1 = 1
2x = 0
x = 0
so y = 1
300
Solve using elimination. Show your work!
x + 2y = 1
x + y = 2
y = -1
x = 3
300
What is the equation of this linear inequality?
y >= -3x + 4
400
Would the following system have one, none, or infinite solutions? Why?
y = -2x + 1
y = -2x + 4
None. The lines are parallel because they have the same slope but different y-intercepts.
400
Solve using substitution. Show your steps!
y = x - 1
y = x - 2
x - 1 = x - 2
-1 = -2
No Solution
400
Solve using elimination. Show your work!
2y - x = 2
-2y + x = 1
0 = 3
No Solution
400
What is the graph of the linear inequality:
y < 3x -1
500
What would the graph of this system look like, and how many solutions would there be?
y = -3x - 4
y = -6/2x - 4
Infinitely many solutions. The equations are the same, so the lines would coincide, or be on top of each other.
500
Solve using substitution. Show all steps!
y = 2x - 1
y - 10/5x = -1
y = 10/5x -1
y = 2x -1
Both equations are the same, so infinitely many solutions.
500
Solve using elimination. Show all steps.
3x - 2y = 4
x - y = 1
x = 2
y = 1
500
Graph the linear inequality:
y > 2x - 4
