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# Elementary Algebra and Geometry

## Section 1.5: Solutions of Systems of Linear Equations

 # of solutions 0 1 Graph Equations

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?