Flashcard: Systems of Equation

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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 set of values that satisfy all equations in the system.

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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that make all equations true simultaneously.

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What is the elimination method?

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The elimination method is a technique for solving systems of equations by 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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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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

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A system of equations has no solution if the equations represent parallel lines that never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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A system of equations has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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How do you determine if a system of equations has one solution?

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A system of equations has one solution if the lines represented by the equations intersect at exactly one point.

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Add the two equations to eliminate x.

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The solution is (-3, -1).

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How can you represent a word problem as a system of equations?

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Identify the variables, write equations based on the relationships described in the problem, and ensure they represent the same situation.