What happens if we graph a system of equations and the lines are parallel?
-
Upload
edwin-philipps -
Category
Documents
-
view
216 -
download
0
Transcript of What happens if we graph a system of equations and the lines are parallel?
What happens if we graph a system of equations and the lines are
parallel?
y = x
y = x - 1
In this lesson you will determine if a system of two
linear equations in two variables has no solution by
graphing.
Let’s ReviewLet’s Review
Slope Intercept Form of an Equation
y = mx + b
slope y-intercept
Let’s ReviewLet’s Review
Graphing a linear equation
y = 2x + 1
slope y-intercept
Let’s ReviewLet’s Review
y = 2x + 1
Let’s ReviewA Common Mistake
Thinking that all systems of equations must have one solution
Let’s ReviewCore Lesson
Graph the system of linear equations. Determine their solution.
y = 2x y - 4 = 2x + 4 = + 4
y = 2x + 4
Let’s ReviewCore Lesson
Graph the system of linear equations. Determine their solution.
y = 2x
y = 2x+4
Slope: 2, y-intercept: 0
Slope: 2, y-intercept: 4
Let’s ReviewCore Lesson
y = 2x
y = 2x+4
Let’s ReviewCore Lesson
Graph the system of linear equations. Determine their solution.
-x + 2y = 0 2y –x = - 2 +x = +x
2y = x
2 = 2 y = x
+x = +x
2y = x - 2
2 = 2 y = x - 1
Let’s ReviewCore Lesson
Graph the system of linear equations. Determine their solution.
y = x
y = x - 1
Slope: , y-intercept: 0
Slope: , y-intercept: -1
Let’s ReviewCore Lesson
y = x - 1
y = x
Let’s ReviewCore Lesson
y = x - 1
y = x
In this lesson you learned to determine if a system of two
linear equations in two variables has no solution by
graphing.
Let’s ReviewGuided Practice
Find the solution for the system of linear equations y = x – 1 and y = x – 5 by graphing.
Let’s ReviewGuided Practice
y = x - 1
y = x - 5
Let’s ReviewGuided Practice
Find the solution for the system of linear equations y=3x and y=3x-2 by graphing.
Let’s ReviewGuided Practice
y=3x
y= 3x-2
Let’s ReviewExtension Activities
When we solve the systems of equations y=2x and y=2x +1, what is our solution? What does it mean?
Let’s ReviewExtension Activities
How many solutions does the system of equations y=3x+1 and y=3x-2 have? Why?
Let’s ReviewExtension Activities
Create a system of linear equations that have no solutions.
Let’s ReviewQuick Quiz
The solution for the system of linear equations y=2x+1 and y=2x-3 is?a) (-1,1) b) (1,-1) c)(-1,-1) d) no solution
The solution for the system of linear equations y=-x+6 and y=-x-2 is?a) (2,-4) b) (-2,4) c) (-2,-4) d) no solution