What happens if we graph a system of equations and the lines are the same?
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Transcript of What happens if we graph a system of equations and the lines are the same?
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 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 MistakeThinking that all systems of equations
must have one solution
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
y = 2(2x+4)
y = 4x+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
Let’s ReviewCore Lesson
y =x-2+3
y =x+1
y =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 PracticeFind the solution for the system of linear equations y-3x = 3 and y = 3(x+1) by graphing.
Let’s ReviewGuided Practice
y-3x = 3 y =3(x+1)
Let’s ReviewGuided Practice
y =3(x+1)
y-3x = 3
Let’s ReviewGuided PracticeFind the solution for the system of linear equations y=2x-2+4 and y=2(x+1) by graphing.
Let’s ReviewGuided Practicey=2x-2+4 y= 2(x+1)
Let’s ReviewGuided Practicey=2x-2+4
y= 2(x+1)
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.
Let’s ReviewQuick Quiz
The solution for the system of linear equations y=2x+1 and y=2x-3 is?a) One solution b)Infinitely Many Solutions
The solution for the system of linear equations y=4x-12and y=4(x+3)is?a) One solution b) Infinitely Many Solutions