I can solve a system of equations by graphing and using tables. 3-1 Linear Systems Unit Objectives Solve a system of equations graphically and algebraically. Solve a system of linear inequalities. Model situations with linear systems Today’s Objective: I can solve a system of equations by graphing and using tables.

If the sharks growth rate stays the same, at what age would they be the same length and how long will they be?

Solving a System using a graph: System of Equations: Two or more equations Solution of a System: Points that make all the equations true. 𝑦= 3 2 𝑥+4 1. Graph the equations - change to y = mx + b - graph the intercepts 2. Find the point of intersection −3𝑥+2𝑦=8 3𝑥+2𝑦=−4 𝑦=− 3 2 𝑥−2 Calculator: Put equations in [y =] Adjust [window] to see intersection. [2nd], [trace], [5] (intersection) [enter], [enter], [enter] (−2, 1)

Solving a System using a graph: 1. Graph the equations 2. Find the point of intersection Solving a System using a graph: 𝑦= 1 2 𝑥−2 𝑥−2𝑦=4 3𝑥+𝑦=5 Calculator: Put equations in [y =] Adjust [window] to see intersection. [2nd], [trace], [5] (intersection) [enter], [enter], [enter] 𝑦=−3𝑥+5 Table: Put equations in y = [2nd], [graph] Scroll to matching y values (2, −1)

Classifying a system Consistent: has a solution Inconsistent: has no solution Independent: one solution Dependent: infinite solutions Same slopes Different y-intercepts Same slopes Same y-intercepts Different slopes −2𝑥+4𝑦=6 −4𝑥+8𝑦=−12 = 𝑦=0.5𝑥+1.5 𝑦=0.5𝑥−1.5 Inconsistent

Graph on graph paper, then check on calculator. x = years y = length 𝑦=0.75𝑥+37 𝑦=1.5𝑥+22 If the sharks growth rate stays the same, at what age would they be same length and how long will they be? 3-1 p.138:7-13 odd, 17-37 odd Graph on graph paper, then check on calculator. 20 years and they will be 52 cm long

Extra word problems

System of Equations A local gym offers two monthly membership plans. Visits Plan A Plan B Plan A: One-time sign-up fee of $100 and charges $5 each time you use the gym. v 100 + 5v 10v 20 200 200 Plan B: No sign-up fee but charges $10 each time you use the gym. When will the two plans cost the same? First day lesson before section 2.2

Example 2 Josie makes and sells silver earrings. She rented a booth at a weekend art fair for $325. The materials for each pair of earrings cost $6.75, and she sells each pair for $23. Write two equations to model the cost and income for Josie. Create a table and graph to find the solution. What does this solution mean? x = Number of earrings y = Dollars made or spent The solution is where Josie will break even. Earrings Cost Income x 325 + 6.75x 23x 20 460 460

Example 3 Edna leaves the trailhead to hike 12 miles toward the lake. Maria leaves the lake to hike towards the trailhead. Edna walks uphill at 1.5 miles/hour, while Maria walks downhill at 2.5 miles/hour. write two equations to model both girls time and distance they are hiking. (Be sure define your variables) Create a table and graph to find the solution. What does this solution mean? t = time spent hiking d = distance traveled from trailhead The solution is where Edna and Maria will meet. time Edna Maria t 1.5t 12 – 2.5t 3 4.5 4.5