Solving Linear Equations and Systems
Warm Up 116
Solve.
6n + 4 = n – 11
Determine whether each
linear relationship is
proportional. If so, state the
constant of proportionality.
Write an equation in slope-
intercept form for the graph of
the linear function.
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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.
System of Linear Equations
Sometimes it is difficult to identify the
exact solution to a system by graphing. In
this case, you can use a method called
substitution
.
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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.
Graph and/or Substitute
Solve the system by substitution and graphing.
EXAMPLE 1
: Solving a System of Equations
by Substitution and Graphing
y =
3
x
y =
x
– 2
Step 1
Write equations as one
equation by substituting
Step
2
Solve for the variable
Step 3
:
Substitute in one of the
original equations.
Ordered Pairs
Solve the system by substitution and graphing.
– 5
-5
2
x +
5
=
x
+ 3
EXAMPLE 2
: Solving a System of Equations
by Substitution and Graphing
Ordered Pair
Substitute in one of
the original equations
Explore solving linear equations and systems through graphing and substitution methods. Understand how to write equations in slope-intercept form, analyze proportional relationships, and determine solutions to systems of equations. Practice using ordered pairs and identifying constant proportions.
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Presentation Transcript
Solve. 6n + 4 = n 11 Warm Up 116 Write an equation in slope- intercept form for the graph of the linear function. Determine whether each linear relationship is proportional. If so, state the constant of proportionality.
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. Step 3: Substitute in one of the original equations. y = 3x y = x 2 Step 1 Write equations as one equation by substituting Ordered Pairs Step 2 Solve for the variable
EXAMPLE 2: Solving a System of Equations by Substitution and Graphing Solve the system by substitution and graphing. 2x + 5 = x + 3 5 -5 2x = x 2 x x x = 2 Substitute in one of the original equations Ordered Pair
