# Section 1.2 Linear Equations and Rational Equations

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Section 1.2 Linear Equations and Rational Equations

Solving Linear Equations in One Variable

Example Solve and check:

Example Solve and check:

Finding Intersection on a Graphing Calculator
Let’s find the intersection of the two lines. Press 2nd Trace to get Calc. Then press #5 for Intersection. Keep pressing enter (three times) to answer the questions and the final result will be the intersection point (1,3). (1, 3) Questions about curves and quesses Find the answer at the bottom of the screen.

Using your calculator and the intersection function find the solution to the following problem.

Linear Equations with Fractions

Example Solve and check:

Rational Equations

A rational equation is an equation containing one or more rational expressions. In the previous example we saw a rational equation with constants in the denominators. That rational equation was a linear equation. The rational equation below is not a linear equation. The solution procedure still involves multiplying each side by the least common denominator. We must avoid any values of the variable that make a denominator zero.

Example Solve and check:

Types of Equations

An equation that is true for all real numbers for which both sides are defined is called an identity. An example of an identity is X+3=X+2+1 An equation that is not an identity, but that is true for at least one real number, is called a conditional equation. 2X=8 An inconsistent equation is an equation that is not true for even one real number. An example of an inconsistent equation is X=X+7

Example Solve and determine if the equation is an identity, a conditional equation or an inconsistent equation.

Solve and check: (a) (b) (c) (d)

Solve the equation. (a) (b) (c) (d)