Systems of Equations Word Problems

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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 a system of equations has one solution?

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It means the lines represented by the equations intersect at exactly one point.

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

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It means the lines represented by the equations are parallel and never intersect.

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

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It means the lines represented by the equations are the same line, thus they intersect at every point on that line.

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What is the substitution method in solving systems of equations?

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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 is the elimination method in 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 is the graphical method for solving systems of equations?

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The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) of intersection.

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How do you determine if two lines are parallel?

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Two lines are parallel if they have the same slope but different y-intercepts.

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How do you determine if two lines are perpendicular?

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Two lines are perpendicular if the product of their slopes is -1.

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What is the standard form of a linear equation?

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