5.44 Setting up ~ 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 set of values that satisfy all equations in the system.

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How do 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 ensure the equations reflect the problem's constraints.

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What does it mean for two variables to be dependent?

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Two variables are dependent if the value of one variable can be expressed as a function of the other, meaning they are related.

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What does it mean for two variables to be independent?

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Two variables are independent if the value of one variable does not affect the value of the other, meaning they are not related.

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How do you solve a system of equations graphically?

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Graph each equation on the same coordinate plane. The point where the lines intersect represents the solution to the system.

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What is substitution in solving systems of equations?

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

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What is elimination in 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 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.