Objective: To solve a system of linear equations by graphing and substitution.

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Presentation transcript:

Objective: To solve a system of linear equations by graphing and substitution

1. System of Equations - is a set of two or more equations with the same variables. 2. Solve a System by Graphing - graph the equations on the same coordinate plane and find the point of intersection

3. Consistent and Independent – when a system of equations has exactly one solution. 4. Consistent and Dependent – when a system of equations has infinitely many solutions. The lines are coinciding.

Classifications of Systems 5. Inconsistent – when a system of equations has no solutions. The lines are parallel.

 Graph each system of equations to find their point of intersection. State the solution. 1. y = 2x – 3 y = -3x +7 These two lines intersect at the point (2, 1) which is the solution to the system of equations. (consistent and independent)

2. y = x + 5 2x – 2y = -4 -2y = -2x – 4 The two lines are parallel (they have the same slope but different y-intercepts) so there is NO SOLUTION. (inconsistent) y = x + 2

Solve a System by Graphing Solve problem 3 and 4 by graphing. 3. y = 2x 4. 2x + y = 3 x + y = 12 y = 2x + 3 Solution: (4, 8) consistent and independent Solution: (0, 3) consistent and independent

 Substitution means to replace one item with another of equal value. 10. y = (x – 7) y = 10 – 5x The second equation tells us that y is equal in value to 10 – 5x, so we can substitute 10 – 5x where we see y in the first equation. 10 – 5x = (x – 7) 10 – 5x = x – 5x = 3x x = -33 x = 33 8 Substitute 33 for x in 8 either equation to find y. y = 10 – 5(33) 8 y = Solution:

12. y = -1.5x + 7 2y = -3x + 14 The first equation tells us that y is equal in value to -1.5x + 7, so we can substitute -1.5x + 7 where we see y in the second equation. 2(-1.5x + 7) = -3x x + 14 = -3x = = 14 is a TRUE statement so these two lines would coincide (be the same line) and we have INFINITE SOLUTIONS (consistent and dependent)

NO Look at the cost line above the income line where x = 25 pogo sticks.

YES About $ That is where the Costs line and Income line have a common point. Finish problems 5 – 9 and 11 on the worksheet.