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4 4 special linear systems

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This document discusses solving systems of linear equations graphically and algebraically. It explains that a system will have one solution if the lines intersect at one point, infinitely many solutions if the lines are the same or parallel, and no solution if the lines do not intersect. Algebraically, a system has infinitely many solutions if the equations are always true and no solutions if they are never true. Two examples of solving systems algebraically are shown.

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4-4 SPECIAL LINEAR SYSTEMS
WHEN GRAPHING: Remember: Lines intersect at one point. One Solution Both are same line. Infinitely Many Solutions Two parallel lines. No Solution
SOLVING ALGEBRAICALLY If you end up with something that is ALWAYS true: System has infinitely many solutions. Examples: 0 =0 2 = 2 -7 = -7 etc
If you end up with something that is NEVER true: System has no solutions. Examples: -5 =1 0 = 3 -2 = 2 etc
EXAMPLE Solve: 4x + 8y = 36 12x + 24y = 108
EXAMPLE Solve: y = 3x + 1 -3x + y = -5
YOU TRY! Solve: 2x + y = 5 4x + 2y = 0

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4 4 special linear systems