Systems of Equations (All three methods)

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What are the three methods to solve a system of equations?

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The three methods are: 1) Graphing, 2) Substitution, 3) Elimination.

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What does it mean if two lines in a system of equations are parallel?

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If two lines are parallel, it means they have no solutions because they never intersect.

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What does it mean if two lines in a system of equations are the same line?

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If two lines are the same, it means there are infinitely many solutions because every point on the line is a solution.

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How do you solve a system of equations using substitution?

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To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation.

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How do you solve a system of equations using elimination?

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To solve using elimination, manipulate the equations to eliminate one variable by adding or subtracting the equations.

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection points of the lines representing the equations.

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What does it mean if a system of equations has no solution?

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It means the lines are parallel and do not intersect.

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What does it mean if a system of equations has one solution?

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It means the lines intersect at exactly one point.

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What is the substitution method?

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The substitution method involves solving one equation for a variable and substituting that value into the other equation.