![]() We represent the linear equation in y=mx+b form, also known as the y-intercept form. If the two graphs are parallel-that is, if there is no point of intersection-then the system is called an inconsistent system, and its solution is expressed as an empty set, or the null set, ⊘.Linear equations are algebraic equations in which each term has a real constant and the equation contains 2 variables of the highest power 1. ![]() If the two graphs coincide-that is, if they are actually two versions of the same equation-then the system is called a dependent system, and its solution can be expressed as either of the two original equations. For those reasons, graphing is used least frequently of all the solution methods. Solving systems of equations by graphing is limited to equations in which the solution lies close to the origin and consists of integers even then, that solution is an approximation solved by eyeballing. The ordered pair at the point of intersection becomes the solution (see Figure 1). To solve using graphing, graph both equations on the same set of coordinate axes and see where the graphs cross. Solve this system of equations by graphing. Linear Equations: Solutions Using Graphing with Two Variables ![]() Quiz: Binomial Coefficients and the Binomial Theorem.Binomial Coefficients and the Binomial Theorem.Quiz: Definition and Examples of Sequences.Quiz: Exponential and Logarithmic Equations.Systems of Inequalities Solved Graphically.Quiz: Systems of Equations Solved Graphically.Systems of Equations Solved Graphically.Quiz: Systems of Equations Solved Algebraically.Systems of Equations Solved Algebraically.Quiz: Solving Equations in Quadratic Form.Quiz: Solving Quadratics by the Quadratic Formula.Solving Quadratics by the Quadratic Formula.Quiz: Solving Quadratics by Completing the Square.Solving Quadratics by Completing the Square.Quiz: Solving Quadratics by the Square Root Property.Solving Quadratics by the Square Root Property.Quiz: Adding and Subtracting Radical Expressions.Adding and Subtracting Radical Expressions.Quiz: Proportion, Direct Variation, Inverse Variation, Joint Variation.Proportion, Direct Variation, Inverse Variation, Joint Variation.Quiz: Adding and Subtracting Rational Expressions.Adding and Subtracting Rational Expressions.Quiz: Trinomials of the Form ax^2 + bx + c.Quiz: Trinomials of the Form x^2 + bx + c.Quiz: Adding and Subtracting Polynomials.Quiz: Linear Equations: Solutions Using Determinants with Three Variables.Linear Equations: Solutions Using Determinants with Three Variables.Quiz: Linear Equations: Solutions Using Matrices with Three Variables. ![]() Linear Equations: Solutions Using Matrices with Three Variables.Linear Equations: Solutions Using Elimination with Three Variables.Quiz: Linear Equations: Solutions Using Elimination with Three Variables.Quiz: Linear Inequalities: Solutions Using Graphing with Two Variables.Linear Inequalities: Solutions Using Graphing with Two Variables.Quiz: Linear Equations: Solutions Using Determinants with Two Variables.Linear Equations: Solutions Using Determinants with Two Variables.Quiz: Linear Equations: Solutions Using Matrices with Two Variables.Linear Equations: Solutions Using Matrices with Two Variables.Quiz: Linear Equations: Solutions Using Elimination with Two Variables.Linear Equations: Solutions Using Elimination with Two Variables.Quiz: Linear Equations: Solutions Using Substitution with Two Variables.Linear Equations: Solutions Using Substitution with Two Variables.Quiz: Linear Equations: Solutions Using Graphing with Two Variables.Linear Equations: Solutions Using Graphing with Two Variables.Quiz: Slopes of Parallel and Perpendicular Lines.Slopes of Parallel and Perpendicular Lines.
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