M2T3 Flashcard2: Solving Systems of Equations

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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 point(s) where the equations intersect.

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What does it mean if two equations are parallel?

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Two equations are parallel if they have the same slope but different y-intercepts, resulting in no solutions.

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How do you find the solution to a system of equations graphically?

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To find the solution graphically, plot both equations on the same graph and identify the point(s) where they intersect.

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What is the substitution method for solving systems of equations?

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The substitution method involves 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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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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

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

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(4, 8)

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(2, 1)

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(7, 4)

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(5, -5)