Types of Solution
If two equations have different slopes, how many solutions will it have?
One
What is the solution to the following system of equations.
y = (1/4)x - 3
y = 2x + 4
(-4, -4)
What is the solution to the following system of equations.
-2x + 4y = 12
7x - 4y = -22
(-2, 2)
What is the solution to the following system of equations.
6x - 6y = 12
x = 2
(2, 4)
If a system of equations has two equations with the same slope and same y-intercept, how many solutions will it have?
Infinite Number of Solutions
What is the solution to the following system of equations.
y = x - 3
y = -6x + 4
(1, -2)
What is the solution to the following system of equations.
5x - 3y = -19
5x - 2y = -11
(1, 8)
What is the solution to the following system of equations.
-2x - 9y = 24
y = -4x + 12
(4, -4)
If a system of equations has two equations with different y-intercepts but the same slope, how many solutions will it have?
No Solutions.
What is the solution to the following system of equations.
y = 2x + 3
x = 4
(4, 11)
What is the solution to the following system of equations.
-8x + 8y = -24
-8x - 8y = 24
(0, -3)
x = 3y + 23
-7y - 7x = -21
(8, -5)
What type of solution would the following system of equations have?
y = 4x + 5
y= -4x + 5
One
Different Slopes
What is the solution to the following system of equations.
y = (-5/2)x - 3
y = (-1/2)x + 1
(-2, 2)
What is the solution to the following system of equations.
3x - 5y = -15
3x - 5y = -5
No Solution
y = 4x + 30
9x - 14y = 3
(-9, -6)
How many solutions would the following system have?
y = -2x + 8
-16 + 2y = -4x
(Hint: Re-arrange)
Infinite Solutions
Same Slope and Y-Intercept
What is the solution to the following system of equations. (Hint: Rearrange)
9x + 3y = -3
y = x + 3
(-1, 2)
What is the solution to the following system of equations. (Hint: Multiply one equation by something to get the same x's or y's.)
6x + 2y = 20
-9x - 12y = 15
(5, -5)
What is the solution to the following system of equations. (Hint: Solve one equation for either"x" or "y".)
-6x - 9y = -3
x + 7y = 17
(-4, 3)