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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How do you solve a system of equations using substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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What does it mean to solve a word problem involving systems of equations?

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It means translating a real-world scenario into mathematical equations and finding the values of the variables that satisfy all equations.

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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 variable.

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

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Identify the variables and what they represent in the context of the problem.

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How can you check your solution to a system of equations?

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Substitute the values of the variables back into the original equations to see if they hold true.

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What is a consistent system of equations?

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A consistent system has at least one solution, meaning the equations intersect at one or more points.

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

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What is a dependent system of equations?

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A dependent system has infinitely many solutions, meaning the equations represent the same line.

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Translate this word problem into equations: 'The sum of two numbers is 10 and their difference is 2.'

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x + y = 10 and x - y = 2.