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.

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

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).

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

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

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

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

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

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

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

Work Schedule: x = hours as lifeguard x + y = 18 8x + 6y = 124 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

You Try!! x = MC ?’s x + y = 20 4x + 6y = 100 y = Problem solving ?’s 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

Homework Finish Homework sheet!