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Elementary Algebra and Geometry

Section 1.5: Solutions of Systems of Linear Equations

# of solutions   0 1

Solving systems of equations

Ex.1 (#12) Solve the system of equations

1. Substitution method


2. Elimination method


3. Equating two equations: can use only if both equations are given in the form of either y = … or
x = …


Ex.2 (#16) Solve the system of equations


Ex.3 (#22) Solve the system of equations


Three equations in three variables

* Left-to-right elimination method (will be discussed when we study chapter 3)
* Substitution method

Ex.4 (#32) Solve the system of equations

Application problems
Ex.5 (#37) One safe investment pays 10% per year, and a more risky investment pays 18% per year. A
woman who has $145,600 to invest would like to have an income of $20,000 per year from her investments.
How much should she invest at each rate?


Ex.6 (#44) A biologist has a 40% solution and a 10% solution of the same plant nutrient. How many cubic
centimeters of each solution should be mixed to obtain 25 cc of a 28% solution?