Download Section 6.1 – Section 6.3 – Systems of Linear Equations – Graphs

Section 6.1 – Section 6.3
Systems of Linear Equations – Graphs and Solving
A Unique Solution
No Solution
Infinitely Many Solutions
Section 6.1 – Section 6.3 – Systems of Linear Equations – Graphs and Solving
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Solving Linear Systems of Equations
Systems of linear equations may be solved graphically or algebraically. When solving
algebraically, we can use either the substitution method or elimination method.
Substitution Method
1. Solve one equation for one variable.
2. Substitute this expression into the other equation for that variable solve for in step 1. This
will give an equation in one variable.
3. Solve the equation.
4. Substitute back to find the value of the other variable.
Example 1: Solve the given system of linear equations, then describe the solution set for the
system.
x + 2y =
8
2x − 4 y =
0
Elimination Method
1. Choose a variable to eliminate. Multiply one or both equations by a nonzero constant, then
add the two equations.
2. Solve the resulting equation.
3. Substitute back to find the value of the other variable.
Example 2: Solve the given system of linear equations, then describe the solution set for the
system.
3x − 6 y =
12
− x + 2 y =−4
Section 6.1 – Section 6.3 – Systems of Linear Equations – Graphs and Solving
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Example 3: Solve the given system of linear equations, then describe the solution set for the
system.
3x − 5 y =
0
2x − 3y =
1
Example 4: Solve the given system of linear equations, then describe the solution set for the
system.
x + 4y =
14
2x − y =
4
Section 6.1 – Section 6.3 – Systems of Linear Equations – Graphs and Solving
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Example 5: Solve the given system of linear equations, then describe the solution set for the
system. Graph the system.
=
y 2x − 3
y=
−3 x + 2
Section 6.1 – Section 6.3 – Systems of Linear Equations – Graphs and Solving
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