Download Warm Up 116 Solve. 6n + 4 = n – 11 Determine whether each linear

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Transcript
Solve.
6n + 4 = n – 11
Determine whether each
linear relationship is
proportional. If so, state the
constant of proportionality.
Warm Up 116
Write an equation in slopeintercept form for the graph of
the linear function.
Standards
• 8.EE.8
Analyze and solve pairs of simultaneous linear equations.
• 8.EE.8b
Solve systems of two linear equations in two variables
algebraically, and estimate solutions by graphing the
equations. Solve simple case by inspection.
• 8.EE.8c
Solve real-world and mathematical problems leading to
two linear equations in two variables.
To
• solve a system of equations
by graphing
• solve a system of equations
by substitution
System of Linear Equations
A system of linear equations is a set of two or more
linear equations containing two or more variables.
A solution of a system of linear equations with two
variables is an ordered pair that satisfies each equation
in the system.
Graph and/or Substitute
Sometimes it is difficult to identify the
exact solution to a system by graphing. In
this case, you can use a method called
substitution.
The goal when using substitution is to
reduce the system to one equation that has
only one variable.
Graph and/or Substitute
Not all systems of linear equations have graphs that
intersect in one point.
There are three possibilities for the graph of a system of two
linear equations, and each represents a different solution
set.
EXAMPLE 1: Solving a System of Equations
by Substitution and Graphing
Solve the system by substitution and graphing.
y = 3x
y=x–2
Step 3: Substitute in one of the
original equations.
Step 1 Write equations as one
equation by substituting
Step 2 Solve for the variable
Ordered Pairs
EXAMPLE 2: Solving a System of Equations
by Substitution and Graphing
Solve the system by substitution and graphing.
2x + 5 = x + 3
–5
2x
−x
x = −2
-5
=x− 2
−x
Substitute in one of
the original equations
Ordered Pair