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Unit 9 Section 6.1-6.3 Notes
Section 6.1 Vocabulary
90. System of Linear Equations: a set of two or more _________________
_________________ containing two or more variables.
91. Solution of a System of Linear Equations: is an ____________ ____________ that satisfies
each equation in the system. This is the intersection point of two lines.
NOTE: Systems of linear equations are used to represent situations and solve problems involving
consumer economics, finance, and geometry.
Section 6.1 Notes (Solving Systems by Graphing)
EQ:
I. Identifying Solutions of Systems
(Recall a solution is an ordered pair that makes both equations true.)
Example: Tell whether the ordered pair is a solution of the given system.
a. (4, 1); x + 2y = 6
x–y=3
Check the ordered pair in both equations
4 + 2(1) = 6
6=6
4–1=3
3=3
Since the ordered pair made both equations true it is a solution for the system. The ordered
pair is the intersection of the two lines.
Try: (-1, 2); 2x + 5y = 8
3x – 2y = 5
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II. Solving a System of Linear Equations by Graphing
(Recall that to graph a line you plot the y-intercept and use the slope to find additional
points on the line)
Example: Solve each system by graphing. Check your answer.
a. y = x – 3
y = -x – 1
b. x + y = 0
y = -1/2x + 1
c. y = -2x – 1
y=x+5
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d. y = 1/3x – 3
2x + y = 4
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Section 6.2 Notes (Solving Systems by Substitution #92)
EQ: How do you solve a linear system using substitution?
Note: In the substitution method we are going to substitute one equation into the other.
Example: Solve each system by substitution
a. y = 2x
y=x+5
b. 2x + y = 5
y=x–4
c. x + 4y = 6
x+y=3
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d. 4y – 5x = 9
x – 4y = 11
Try: 2x + y = -4
x + y = -7
-2x + y = 8
3x + 2y = 9
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Section 6.3 Notes (Solving Systems by Elimination #93)
Note: In the elimination method we will be “eliminating” one of the terms in the equations.
EQ: How do you solve a linear system using elimination?
Example: Solve each system using elimination.
a.
x – 2y = -19
5x + 2y = 1
b. 3x + 4y = 18
-2x + 4y = 8
c. 2x + y = 3
-x + 3y = -12
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d. 7x – 12y = -22
5x – 8y = -14
Try:
3x + 3y = 15
-2x + 3y = -5
2x + 5y = 26
-3x – 4y = -25