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Graph of a Line
Sum of the Roots of a Quadratic
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Writing Linear Equations Using Slope and Point
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Solving Equations 3
Solving Quadratic Equations
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nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Percents
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
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Polar Form of a Complex Number
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Algebra
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Higher Degrees and Variable Exponents
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Writing a Rational Expression in Lowest Terms
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The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
fractions
Rotating an Ellipse
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Linear Equations
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Combining Operations
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Graphing Inequalities in Two Variables
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Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
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Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
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Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Quadratics
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
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Simplifying Expressions Involving Variables
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Decimals
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
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Solving Linear Equations Graphically

To solve a linear equation graphically,

  1. Write two functions using each expression in the equation as a rule.
  2. Graph both functions on the same coordinate plane.
  3. Determine the point of intersection.

The solution of the equation is the x -coordinate of the point of intersection.

The y -coordinate is the value obtained for both expressions when the equation is evaluated with the solution.

Example:

2x + 3 = x + 5

1. y1 = 2 x + 3; y 2 = x + 5

2.

3. (2, 7); solution is 2

Try the following:

1) 3x + 5 = 2x

2) 6x - (4x + 3) = 7 - 3x

There are three possibilities when solving linear equations:

  1. One solution exists when the graphs intersect.
  2. No solution exists when the graphs are parallel.
  3. An infinite number of solutions exist when the graphs coincide.
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