2. Lecture objectives:
• Solve systems of linear equations exactly and approximately
• Determine which type of systems can be solved using
substitution
• Find the point of intersection
• Graph the system of equations
3. 3 Methods to Solving Systems of Equations
1. Substitution
2. Elimination
3. Graphing
4. The Substitution Method
• The substitution method is a simple way to solve linear
equations algebraically and find the solutions of the
variables.
• The substitution method requires solving for one variable,
and then substituting that expression into the second
equation.
5. Example 1: Solve the system of equations using the
substitution method.
y = 5
-3x + 4y = 8
Step 1: Solve for x or y in one of the
equations.
Step 2: Substitute the expression
from the first equation into the other.
Then solve.
Step 3: Plug the solution into either
equation to find the other variable.
Step 4: Write your solution as an
ordered pair.
7. Video Clips
Please watch these step-by-step videos on how to solve a system of
equations using the substitution method.
8. Now You Try (1)
Solve the system of equations using the substitution method.
1. y = 5x − 7
−3x − 2y = −12
9. Now You Try (1)
Solve the system of equations using the substitution method.
1. y = 5x − 7 (2, 3)
−3x − 2y = −12
10. Example 2: Solve the system of equations using the
substitution method.
-5x + y = -2
-3x + 6y = -12
Step 1: Solve for x or y in one of the
equations.
Step 2: Substitute the expression
from the first equation into the other.
Then solve.
Step 3: Plug the solution into either
equation to find the other variable.
Step 4: Write your solution as an
ordered pair.
12. Now You Try (2)
Solve the system of equations using the substitution method.
2. x + 3y = 1
−3x − 3y = −15
13. Now You Try (2)
Solve the system of equations using the substitution method.
2. x + 3y = 1 (7, -2)
−3x − 3y = −15
14. Example 3: For each question, solve the system of equations
by substitution and plot the point of intersection on the
graph.
5x + 3y = 9
2x − 3y = 12
Step 1: Solve for x or y in one of the
equations.
Step 2: Substitute the expression
from the first equation into the other.
Then solve.
Step 3: Plug the solution into either
equation to find the other variable.
Step 4: Write your solution as an
ordered pair.
17. Now You Try (3)
Solve the system of equations using the substitution method and plot the
point of intersection on a graph.
3. -2x + 6y = 6 (3, 2)
-7x + 8y = -5
4. y = x – 4 (4, 0)
-4x - 6y = -16
5. 6x + 6y = -6 (-3, 2)
5x + y = -13