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Lesson 2 –Linear Systems LINEAR SYSTEMS Two or more lines considered together The solution to a linear system is the point(s) of intersection (POI) There are 3 possible outcomes when solving a linear system. ONE SOLUTION INFINITE SOLUTIONS Solution is a point Solution is a line Equivalent Systems NO SOLUTIONS No solution Example ① Graph the linear system below. −𝑥 + 2𝑦 = 6 1 𝑦 = 𝑥+3 2 What is the solution to the linear system? Is there a way you can tell if you will have one, none, or infinite solutions without graphing? Example ② a) Without graphing, determine whether each system has one solution, no solution or infinitely many solutions. 𝑥 + 3𝑦 = −1 2𝑥 + 6𝑦 + 2 = 0 Example ③ c) 3𝑥 + 2𝑦 – 10 = 0 2𝑥 – 3𝑦 – 3 = 0 Create an equivalent linear equation for each of the following: a) 𝑦 = 3𝑥 – 7 Example ④ b) 𝑦 = 2𝑥 – 3 2𝑥 – 𝑦 = 5 b) 𝑥 – 4𝑦 + 12 = 0 Graph each equation on the same set of axes to find the point of intersection: 𝑦 = 2𝑥 + 1 𝑦 + 𝑥 = 7