Solving Systems by Substitution

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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

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It involves solving one equation for one variable and substituting that expression into the other equation.

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What is an infinite solution in a system of equations?

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It means that there are countless solutions that satisfy both equations, often when the equations represent the same line.

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

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It means that the equations represent parallel lines that never intersect.

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How do you isolate a variable in an equation?

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You manipulate the equation using algebraic operations to get the variable on one side by itself.

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What is the first step in solving a system of equations by substitution?

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Choose one equation and solve for one variable in terms of the other variable.

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What does it mean for two equations to be dependent?

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It means they represent the same line, resulting in infinite solutions.

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What is the graphical representation of a system of equations?

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The solution is represented by the point(s) where the lines intersect on a graph.