Mary Jane Sterling - Algebra II - 1001 Practice Problems For Dummies (+ Free Online Practice)

626–630 Sketch the graph of the ellipse.

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631–640 Write the equation of each hyperbola in standard form, either or .

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641–645 Determine the center, foci, and equations of the asymptotes of the hyperbola.

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646–650 Sketch the graph of the hyperbola.

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Chapter 11

A linear equation consists of variable terms whose exponents are always the number 1. When you have two variables, the equation can be represented by a line. With three terms, you can draw a plane to describe the equation. More than three variables is indescribable, because there are only three dimensions. When you have a system of linear equations, you can look for the values of the variables that work for all the equations in the system — the common solutions. Sometimes there’s just one solution, sometimes many, and sometimes there’s no solution at all.

In this chapter on systems of linear equations, you’ll see the following:

Determining the point of intersection of two lines

Finding a single point of intersection of three planes

Writing expressions for multiple solutions of systems

Writing systems in the echelon form or reduced row echelon form

Decomposing fractions using systems of linear equations

Don’t let common mistakes trip you up; watch for the following ones when working with systems of linear equations:

Trying to eliminate more than one variable when solving a system

Distributing negative numbers incorrectly over several terms

Writing the coordinates of ordered pairs and ordered triples in the incorrect positions

Placing the incorrect numerator over its denominator when decomposing fractions

651–660 Solve the system of two linear equations for x and y.