3F Systems of Equations - Word Problems 1 5Q

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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 solve a system of equations using substitution?

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To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

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What does it mean to find the intersection of two lines in a graph?

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Finding the intersection of two lines means determining the point where the two lines cross, which represents the solution to the system of equations.

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What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation graphs as a straight line and has no exponents greater than one, while a nonlinear equation can graph as a curve.

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

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The first step is to define the variables that represent the unknown quantities in the problem.

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

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You can check the solution by substituting the values back into the original equations to see if they hold true.

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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.

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What does it mean if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines that never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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How do you set up equations from a word problem?

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Identify the relationships described in the problem, define variables, and translate the relationships into mathematical equations.