University:
Highline College
Course:
MATHP 141 | Precalculus I Plus Extra Support
Academic year:

2022
Views:

256

Pages:

2
Author:

Reynaldo Wong

Workshop #7 1. (a) Give the equation for a line which passes through the origin and the point (2, 7). (b) Give the equation for a line which passes through the point (−1, 4) and (0, 6). (c) At which point (if at all) do these lines intersect? 2. If possible, solve the systems by elimination 2x + 3y = 1 (a) x + 3y = 2 2 x + 12 y = 12 (b) 3 2x − y = 1 (c) (d) 4x + y = 6 2 1 3x + 6y = 1 1 x 1 x + − 1 y 1 y = = 5 9 1 9 3. If possible, solve the following systems using substitution 2y − 4 = 3x y = 32 x (a) (c) 6x − 4y = −4 2x + 3y = 5 3 x + 23 y = 7 2x + 3y = 8 (b) 43 (d) 1 4x + 6y = 16 5 x − 2 y = 18 4. let x be the number of units in thousands. Suppose C(x) is a linear function whose output is the cost of making x units in thousands of dollars and R(x) is a linear function that gives the revenue if x units are sold in thousands of dollars? y (1.2, 234) C(x) R(x) x (a) What is the signiﬁcance of the point shown? (b) Will the production of these items ever turn a proﬁt? Why or why not? 5. A system of two linear equations is formed by the two lines L1 and L2 . (a) Suppose the system is only solved by the point (3, 7). What does this tell us about L1 and L2 ? (b) Suppose the system isn’t solved by any points. What does this tell us about L1 and L2 ? (c) Suppose the system is solved by the points (1, 2) and (4, 9). What does this tell us about L1 and L2 ? 6. Solve the inequalities graphically (a) y < 2x (b) y ≥ 3 (c) x − 2y < 1 7. Which of the following points satisfy the given system of inequalities (a) (3, 0) (c) (4, −3) (b) (3, −1) (d) (5, −1) 3x + 2y > 6 x + 3y ≤ 2 8. Find the solution set of the system of linear inequalities graphically x+y >1 3x + y ≤ 1 (a) (c) x+y ≤2 −x + 2y > 6 2x − 6y ≤ 12 x2 − y < 0 (b) (d) y + x2 < 2 x − 3y < 6 9. Create a system of linear inequalities whose solution set is the given region. y (1, 3) (8/3, 17/6) (1, 7/8) x