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 occurs when the equations represent the same line, resulting in countless solutions.

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

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It means 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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By performing inverse operations to get the variable alone on one side of the equation.

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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.

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How can you check if your solution to a system of equations is correct?

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Substitute the solution back into both original equations to see if they hold true.

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What is the graphical representation of a system of equations?

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It is the point(s) where the lines representing the equations intersect.

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What does the term 'substitution' refer to in algebra?

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It refers to replacing a variable with an equivalent expression.