solving a system of linear equations… you’ve already learned: we have to learn: 1. graphing2....
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Solving a system of linear equations…
You’ve already learned: We have to learn:
1. Graphing 2. Substitution
3. Elimination
Solving Linear Systems by
Substitution7.2
Objectives for Today:1. Solve a system of equations by
substitution2. Solve systems from the real world
-3x y 9
2x+4y 8
335y2x
-113yx
When we say to solve for one variable…Which is the best variable to use for substitution?
Solve the System by Substitution
Solve a system by substitution:
1. Solve for one of the variables and star it.
Hint: Look for the variable that is already alone OR easy to isolate.
2. Substitute this expression into the other equation.
3. Solve for the only variable.
4. Substitute this value into the starred equation.
5. Clearly state your answer as an ordered pair.
6. Check the answer.
Here’s Our Steps:
Solve the system by substitution.
Solve a system by substitution:
1. Solve for one of the variables and star it.
2. Substitute this expression into the other equation.
3. Solve for the only variable.
4. Substitute this value into the starred equation.
5. Clearly state your answer as an ordered pair.
6. Check the answer.
2y2x
1yx-(-1, 0)
Example 1 Solve the System by Substitution
Solve the system by substitution.
6y5x
142y3x(2, 4)
Example 2 Solve the System by Substitution
Solve a system by substitution:
1. Solve for one of the variables and star it.
2. Substitute this expression into the other equation.
3. Solve for the only variable.
4. Substitute this value into the starred equation.
5. Clearly state your answer as an ordered pair.
6. Check the answer.
Solve the system by substitution.
33yx
374y5x(9, 2)
Example 3 Solve the System by Substitution
Solve a system by substitution:
1. Solve for one of the variables and star it.
2. Substitute this expression into the other equation.
3. Solve for the only variable.
4. Substitute this value into the starred equation.
5. Clearly state your answer as an ordered pair.
6. Check the answer.
Solve the system by substitution.
6x 2y=16
-2x+y=-2 (2, 2)
Example 4 Solve the System by Substitution
Solve a system by substitution:
1. Solve for one of the variables and star it.
2. Substitute this expression into the other equation.
3. Solve for the only variable.
4. Substitute this value into the starred equation.
5. Clearly state your answer as an ordered pair.
6. Check the answer.
In one day, the Baseball Hall of Fame in Cooperstown admits 321 adults and children and collects $1590. The price of admission is $6 for an adult and $4 for a child. How many adults and how many children were admitted to the museum that day.
153 adults & 168 children
Example 5 Real Life Linear System
Solve the system of equations by substitution.
-4x+y=-10
6x+2y=22
Exit Slip To be completed before leaving…
7.2 Practice Worksheet
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