Systems with Graphs
Solving by Substitution
Solving by Elimination
Random
Number of Solutions
100
What is the solution?
(-1,1)
100
Solve the systems of equations:
-3x + 4y = -2
y = -5
(-6, -5)
100
Solve the systems of equations:
14x + 2y = 26
-14x - 6y = -50
(1, 6)
100
What strategy would be best?
14x + 2y = 26
-14x - 6y = -50
Elimination because the coefficients on x are the same number with opposite signs
100
How many solutions does the system have?
3y + 4x = 6
12y + 16x = 24
These are the same exact line, therefore they have
Infinite Solutions
100
Solve using Graphing
y= 2x + 1
y= -x + 7
(2, 5)
100
Solve the systems of equations:
-5x - 5y = 10
y = -4x -17
(-5, 3)
100
Solve the systems of equations:
x -3y = 6
x + 3y = 12
(9,-1)
100
What would a system of equations with infinite solutions look like on a graph?
One line.
100
How many solutions does the system have?
3x - y = 19
-3x + y = 10
No solution
100
Solve Using Graphing:
y = 5/3x + 2
y = -3
100
Solve the systems of equations:
y = -2x - 9
3x -6y = 9
(-3, -3)
100
Solve the systems of equations:
-6x - 10y = 4
6x + 10y = 0
No Solution
100
What would a system of equations with one solution look like on a graph?
Two lines that intersect at one point.
100
How many solutions does the system have?
y=-2x+3
y=-2x+10
No Solution
Same slope different y-intercepts
100
How many solutions are there?
Infinitely Many Solutions
100
Solve the systems of equations:
-8x - 5y = -24
-x + y = 10
(-2, 8)
100
Solve the systems of equations:
-3x - 24y = -66
3x + 4y = -14
(-10, 4)
100
Solve the following System of Equations using ANY method
x = 3y - 5
2x - 3y = -4
(1, 2)
100
How many solutions does the system have?
y=3x-10
y=8x-5
Bonus: solve the solution
One Solution
(-1, -13)
100
Solve the systems of linear equations by graphing:
100
Solve the systems of equations:
-8x + y = -7
16x - 2y = 14
Infinitely Many Solutions
100
Solve the systems of equations:
-15x + 6y = -36
4x - 3y = 11
(2, -1)
100
What would a systems of equations with no solution look like on a graph?
Parallel Lines