Page 201 - ABCTE Study Guide_Neat

A Little About Linear Inequalities

A linear inequality looks just like a linear equation, but the equal sign is replaced by an inequality
sign:

To graph a linear inequality, you would use the same method you used to graph a linear equality, except
for the following: if the equation uses a less than (<) or greater than (>) sign, the line will be dashed
instead of solid. If the equation uses a less than or equal ( ) or greater than or equal sign ( ), the line
will still be solid.

For linear inequalities, you will shade the graph either above or below the line that you have drawn. The
easiest way to determine which part to shade is to choose a point either above or below the line; (0, 0) is
often an easy point to choose. Plug in the values of the point and see if the inequality is true. If it is true,
shade the area that contains the point. If the inequality is false, shade the area on the other side of the
line.

Take a look at the following example to see how it works.

Zero is not greater than four. Therefore, the inequality is false and area to the right of the line is shaded.

Systems of Equations

• A system of equations is a group of two or more linear equations. While a single linear
equation has infinite solutions (all the points along the line), a pair of linear equations has a
single solution or no solution.
• A pair of linear equations has a single solution at the point where the two lines intersect.
This ordered pair is the solution to the system of equations. All pairs of nonparallel lines (that
are not actually the same line in disguise) have exactly one solution.
• A system of parallel lines (lines with the same slope) has no solution because the lines
will never intersect.

Example

What is the solution to the system of equations shown on the graph below?