# 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?