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Daily Essential Question:

Daily Essential Question:. How do I solve a system of Linear equations using the graphing method?. System of 2 linear equations :. 2 equations with 2 variables (x & y) each. Ax + By = C Dx + Ey = F Solution of a System – an ordered pair, ( x,y ) that makes both equations true.

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Daily Essential Question:

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  1. Daily Essential Question: • How do I solve a system of Linear equations using the graphing method?

  2. System of 2 linear equations: • 2 equations with 2 variables (x & y) each. Ax + By = C Dx + Ey = F • Solution of a System – an ordered pair, (x,y) that makes both equations true.

  3. Ex: Check whether the ordered pairs are solutions of the system: x-3y= -5 -2x+3y=10 • (1,4) 1-3(4)= -5 1-12= -5 -11 = -5 *doesn’t work in the 1steqn, no need to check the 2nd. Not a solution. • (-5,0) -5-3(0)= -5 -5 = -5 -2(-5)+3(0)=10 10=10 Solution

  4. Solving a System Graphically • Graph each equation on the same coordinate plane. • If the lines intersect: The point (ordered pair) where the lines intersect is the solution. • If the lines do not intersect: • They are the same line – infinitely many solutions (they have all points in common). • They are parallel lines – no solution (they have no points in common).

  5. Ex 1: Solve the system graphically: y=3x-12 y=-2x+3 (3, -3)

  6. Ex 2: Solve the system graphically: y=-x-1 y=8-x No Solution

  7. Ex 3: Solve the system graphically:x+y=-2 2x-3y=-9 **Put in Slope-Intercept form** (-3,1)

  8. Ex 4: Solve the system graphically: 3x-2y=6 -6x+4y=-12 **Put in Slope-Intercept form** ∞ many

  9. Ex 5: Solve the system graphically: 2x-2y= -8 2x+2y=4 (-1,3)

  10. Ex 6: Solve graphically: x-y=5 2x+2y=10 (5,0)

  11. Setting Up Application Problems Define variables Write as a system of equations Resort Costs: Resort A charges $70 per night, plus a one-time surcharge of $5. Resort B charges $65 per night, plus a one-time surcharge of $20. After how many nights will the total cost be the same? x = number of nights y = 70x + 5 y = 65x + 20 y = total cost

  12. Work Schedule: You worked 18 hours last week and earned a total of $124 before taxes. Your job as a lifeguard pays $8 per hour, and your job as a cashier pays $6 per hour. How many hours did you work at each job? x = hours as lifeguard x + y = 18 8x + 6y = 124 y = hours as cashier

  13. You Try!! A math test is to have 20 questions. The test format uses multiple choice worth 5 points each and problem solving worth 6 points each. The test has a total of 100 points. Write a system to determine how many of each type of question are used. x = MC ?’s x + y = 20 4x + 6y = 100 y = Problem solving ?’s

  14. Homework • Finish Homework sheet!

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