What happens if we graph a system of equations and the lines are the same? y = 2(2x+4) y = 4x+8.
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Transcript of What happens if we graph a system of equations and the lines are the same? y = 2(2x+4) y = 4x+8.
In this lesson you will determine if a system of two
linear equations in two variables has infinitely many
solutions by graphing.
Let’s ReviewCore Lesson
Graph the system of linear equations. Determine their solution.
y = 2(2x+4) y – 4x = 8y = 4x+8 +4x =
+4xy = 4x + 8
Let’s ReviewCore Lesson
Graph the system of linear equations. Determine their solution.
y = 2(2x+4)
y = 4x+8
Slope: 4, y-intercept: 8
Slope: 4, y-intercept: 8
y = 4x+8
Let’s ReviewCore Lesson
Graph the system of linear equations. Determine their solution.
x -y = -1 y =x-2+3y =x+1 -x =-x
-y = -1-x
-1 = -1 y= 1 +x y= x + 1
Let’s ReviewCore Lesson
Graph the system of linear equations. Determine their solution.
y =x+1
y =x-2+3
Slope:1, y-intercept: 1
Slope:1, y-intercept: 1y =x+1
In this lesson you learned to determine if a system of two
linear equations in two variables has infinitely many
solutions by graphing.
Let’s ReviewGuided Practice
Find the solution for the system of linear equations y-3x = 3 and y = 3(x+1) by graphing.
Let’s ReviewGuided Practice
Find the solution for the system of linear equations y=2x-2+4 and y=2(x+1) by graphing.
Let’s ReviewExtension Activities
When we solve the systems of equations y=2x+2 and y=2(x+1), what is our solution? What does it mean?
Let’s ReviewExtension Activities
How many solutions does the system of equations y=-3x-3 and y=-3(x+1) have? Why?
Let’s ReviewExtension Activities
Create a system of linear equations that have infinitely many solutions.