Word Problems - Systems of Equations

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What is a system of equations?

Back

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

Back

Identify the variables, translate the relationships into equations, and express the conditions given in the problem.

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What does it mean for a system of equations to have 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 for a system of equations to have infinitely many solutions?

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It means the equations represent the same line, so every point on the line is a solution.

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How can you determine the price of items from a word problem involving sales?

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Set up equations based on the quantities sold and total sales, then solve the system of equations.

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What is the first step in solving a system of equations?

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The first step is to write the equations in a standard form, usually Ax + By = C.

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What is substitution in the context of solving systems of equations?

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Substitution is a method where you solve one equation for one variable and substitute that expression into the other equation.

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What is elimination in the context of solving systems of equations?

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Elimination is a method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

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What is a variable in a mathematical equation?

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A variable is a symbol (often x, y, or z) that represents an unknown value in an equation.

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How do you check the solution of a system of equations?

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Substitute the solution back into the original equations to see if they hold true.