Test Solving Systems of Equations

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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?

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Finding the values of the variables that satisfy all equations in the system.

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What is the graphical method of solving a system of equations?

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Plotting the equations on a graph and identifying the point(s) where they intersect.

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

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The system has no solution because the lines never intersect.

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

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The system has infinitely many solutions because the lines are the same.

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How do you determine if a point is a solution to a system of equations?

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Substitute the point's coordinates into each equation; if all equations are satisfied, it is a solution.

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What is the substitution method for solving systems of equations?

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Solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method for solving systems of equations?

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

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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.