Special Types of Linear Systems

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Special Types of Linear Systems February 6, 2014 Pages 459-462

7.5 SPECIAL TYPES OF LINEAR SYSTEMS Students will be able to: Solve special systems of linear equations in two variables. Classify systems of linear equations and determine the number of solutions.

Without solving the linear system, tell whether the linear system has one solution, no solution, or infinitely many solutions. 1. 5x + y = – 2 Equation 1 –10x – 2y = 4 Equation 2 SOLUTION Write Equation 1 in slope- intercept form. y = – 5x – 2 Write Equation 2 in slope- intercept form. y = – 5x – 2 ANSWER Because the lines have the same slope and the same y-intercepts, they are the same line and there are infinitely many solutions.

2. 6x + 2 y = 3 6x + 2 y = – 5 SOLUTION 3 y = – 3x + 2 5 y = – 3x – 2 Equation 1 6x + 2 y = – 5 Equation 2 SOLUTION y = – 3x + 3 2 Write Equation 1 in slope- intercept form. y = – 3x – 5 2 Write Equation 2 in slope-intercept form. ANSWER Because the lines have the same slope but different y-intercepts, the lines are parallel and the system has no solution.

3. x – 3y = – 15 2x – 3y = – 18 SOLUTION y = 1 x + 5 3 y = 2 x + 6 3 Equation 1 2x – 3y = – 18 Equation 2 SOLUTION y = 1 x + 5 Write Equation 1 in slope-intercept form. 3 y = 2 x + 6 Write Equation 2 in slope- intercept form. 3 ANSWER Because the lines have different slope and different y-intercepts,the system has one solution.

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