Math 901: Algebra I Unit 1 Test Study Guide

Math 905 Test Study GuideAlgebra I Unit 5: Linear Systems1. Know what a linear system is.2. Identify the graph of a linear system as…• consistent: The two lines intersect in one point.• equivalent: You only see 1 line. The two lines are concurrent (same line).• inconsistent: The two lines do NOT intersect. They are parallel.3. Determine the number of solutions of a linear system as…• no: No solution because the lines do not intersect – they are parallel.This is an inconsistent system.• one: One point of intersection because the lines are in the same planeand have different slopes. This is a consistent system.• infinite: The lines are concurrent. This is an equivalent system.4. Identify and compare the solution sets of graphed linear systems.5. Given a linear system, evaluate three given ordered pairs in the system todetermine which is the correct solution.6. Apply the multiplication property of equality and the addition property ofequality to simplify linear systems.7. Identify the correct graph of the solution of a system of linearinequalities.8. Solve systems of linear equations algebraically (recall the substitutionmethod).9. Be able to identify the x-value solution and the y-value solution of linearsystems.10. Write the solutions of linear systems as ordered pairs.11. Find the determinant of a given 2X2 matrix.12. Given a system of two linear equations in x and y, identify the second rowof entries for the system determinant.13. Calculate the system determinant for a given linear system.14. Given a system of two linear equations in x and y, find the value of they-determinant.15. Solve a given system of two linear equations in x and y, and with generalconstant k. The equations will be of the form, Ax + By = k, where A and Bare integers and k remains the general constant k.16. Solve a word problem involving two unknown numbers by writing and solving alinear system of two equations and two unknowns.

17. Solve a word problem involving the cost of two items in a store by writingand solving a linear system of two equations and two unknowns.18. Given a word problem involving the numerator and denominator of afraction, identify a system of equations that could be used to solve it.2 3 719. Given an equation with rational coefficients, such as x+ y = , identify an5 4equivalent equation with integral coefficients by multiplying the equation bythe lowest common denominator. In this case, we multiply by 20 to get8x+ 15y= 14.20. Given a certain amount of money invested in two accounts with differentinterest rates, calculate the amount of money invested in each account.21. Knowing that distance = rate X time, and given a boat traveling at anunknown speed in a stream with an unknown current, write a system ofequations that represents the trip upstream (against the current), anddownstream (with the current).22. Solve the above system to find the speed of the boat and the speed ofthe current.10