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 graph a system of equations?

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Graphing a system of equations involves plotting each equation on the same coordinate plane to find the point(s) of intersection, which represent the solution(s).

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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 variable.

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

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Identify the variables, translate the relationships and conditions into equations, and then form a system of equations.

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

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Read the problem carefully, identify the variables, and determine the relationships between them.

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Example of a word problem: The sum of two numbers is 10. What are the equations?

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x + y = 10.