Solving Systems by Substitution

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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 does it mean to solve a system of equations by substitution?

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Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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How do you isolate a variable in an equation?

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To isolate a variable, perform inverse operations to get the variable on one side of the equation and all other terms on the opposite side.

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What is the substitution method?

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The substitution method is a technique for solving systems of equations where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the graphical interpretation of a system of equations?

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The graphical interpretation involves plotting the equations on a coordinate plane; the intersection point(s) represent the solution(s) of the system.

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

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If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

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

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If two lines coincide, they are the same line, meaning there are infinitely many solutions to the system.