University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

28

Pages:

4
Author:

anon

Linear Systems What is a Linear System? A linear system is a set of two or more linear equations studied together (at the same time). Point of Intersection (P.O.I) is the point where two or more lines intersect/meat. A solution to a linear system of two equations is a point or a set of points that satisfy both equations. Example 1: a) Solve the following linear system by graphing y=-2/3x+6 and 3x-y-5=0 P.O.I. is (3,4). This is the point where the two lines meet. (3,4) is the solution to the linear. b) Verify that your solution satisfies both equations Substitute (3,4) in (1) and (2) to check whether the L.S. is equal to the R.S. 1) y=-2/3x+6 L.S.=y =4 R.S.=-2/3x+6 =(-2/3)(3)+6 =-2+6 =4 L.S=R.S 2)3x-y-5=0 L.S.=3x-y-5 =3(3)-4-5 =9-9 =0 R.S=0 L.S.=R.S. (3,4) is the correct solution to the linear system. There are three different types of solutions: Two nonparallel lines Two parallel lines Two identical lines Any point on the lines, satisfies the equations ((1) and (2)) So, there is an infinite number of points that satisfy (1) and (2) There is an in infinite (many) number of solutions to this linear system. Example 2: Jack is going to work at the ACC for the summer selling programs. He h as two payment options. Option 1: He gets paid $1 for every program he sells. Option 2: He gets paid $12 per day plus $0.50 for every program he sells. a) Write an equation to represent each payment option. Let E represent Jack`s earnings and let p rep. the number of programs sold. Option 1: E=p Option 2: E=0.50p+12 b) Graph each payment option. c)How should Jack decide which option to choose? (Under what conditions should Ja ck choose each option?) -If he sells less than 24 programs, he should choose option 2 -If he sells exactly 24 programs, he would make $24 with either option. -If he sells more than 24 programs, he should choose option 1. d) What is the point of intersection? What does the point of intersection mean? P.O.I is (24,24) It means that Jack makes $24 when he sells 24 programs. Example 3: The lines y=x-2 and x + y = 6 intersect at a point. Which is the point of intersection? Explain how you know. A (3, 5) B (3, 3) C (2, 4) Solution: Substitute each point in y = x - 2 and x + y = 6 The point that satisfies both equations is the point of intersection D(4,2)