Solve Systems by Substitution or Elimination

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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.

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

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It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What is the substitution method?

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A method 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 elimination method?

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A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

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How do you check the solution of a system of equations?

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Substitute the solution back into the original equations to verify if both equations are satisfied.

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What is a consistent system of equations?

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A system that has at least one solution.

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What is an inconsistent system of equations?

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A system that has no solutions.

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What is a dependent system of equations?

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A system that has infinitely many solutions, where the equations represent the same line.

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Solve by substitution: x - y = 6 and y - 2x = -5. What is the solution?

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(-1, -7)