Solving Systems of Equations

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What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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What does it mean to solve a system of equations by graphing?

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It involves plotting the equations on a graph and identifying the point(s) where they intersect, which represents the solution.

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What is the solution to a system of equations?

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

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What does it mean if two lines on a graph are parallel?

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The system of equations has no solution because the lines never intersect.

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What does it mean if two lines on a graph coincide?

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The system of equations has an infinite number of solutions because the lines are the same.

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What is the elimination method for solving systems of equations?

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A method that 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 for solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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

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If the lines representing the equations intersect at exactly one point on a graph.

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What is the graphical representation of the solution (3, 3)?

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It is the point where x = 3 and y = 3 on a coordinate plane.

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What is the cost equation for a pizza at Palanzio’s Pizzeria?

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y = 6.80 + 0.90x, where y is the total cost and x is the number of toppings.