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Section 3.5: Systems of Linear Equations in Two
Variables
System of Linear Equations:
A set of linear equations in the same 2
variables
Solution:
Any ordered pair of numbers that is a
solution of each equation in the system
Equivalent Systems:
Systems that have the same solution set
Consistent:
A system that has at least one solution
...equations that will intersect
Inconsistent:
A system that has no solution
...equations that are parallel
Algebra 2: Section 3.5
1
Section 3.5: Systems of Linear Equations in Two Variables
Example: Solve the system. If it has an infinite
solution, give 3 solutions.
x + y = 9 ; x - y = 13
Method 1: Substitution
Method 2: Linear Combination
(Stack 'em)
Algebra 2: Section 3.5
2
Section 3.5: Systems of Linear Equations in Two Variables
Example: Solve the system. If it has an infinite
solution, give 3 solutions.
2x - 3y = 7 ; 3x + y = 5
Algebra 2: Section 3.5
3
Section 3.5: Systems of Linear Equations in Two Variables
Example: Solve the system. If it has an infinite
solution, give 3 solutions.
x + y = 3x - 1 ; -2x + y = -1
Algebra 2: Section 3.5
4
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