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**Extra resources for Algebra II (Cliffs Quick Review)**

**Sample text**

One way to graph a linear equation is to find solutions by giving a value to one variable and solving the resulting equation for the other variable. A minimum of two points is necessary to graph a linear equation. Example 6: Draw the graph of 2x + 3y = 12 by finding two random points. To do this, select a value for one variable; then substitute this into the equation and solve for the other variable. Do this a second time with new values to get a second point. Let x = 2; then find y. 2x + 3y = 12 2(2) + 3y = 12 4 + 3y = 12 3y = 8 y = 83 Therefore, the ordered pair (2, 83 ) belongs on the graph.

It will always have an x-coordinate of zero. A vertical line that is not the y-axis will have no y-intercept. One way to graph a linear equation is to find solutions by giving a value to one variable and solving the resulting equation for the other variable. A minimum of two points is necessary to graph a linear equation. Example 6: Draw the graph of 2x + 3y = 12 by finding two random points. To do this, select a value for one variable; then substitute this into the equation and solve for the other variable.

3 - 8=- 5 - 5 =- 5 ✓ ? 2 + 6 =8 8=8✓ The solution is x = 1, y = –2. If the substitution method produces a sentence that is always true, such as 0 = 0, then the system is dependent, and either original equation is a solution. If the substitution method produces a sentence that is always false, such as 0 = 5, then the system is inconsistent, and there is no solution. Linear Equations: Solutions Using Eliminations To solve systems using elimination, follow this procedure. 1. Arrange both equations in standard form with like terms above one another.