Indicator 12-14 Solve Systems of Equations /Word Prob Set Up

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What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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What does it mean for a system of equations to have a unique solution?

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It means there is exactly one set of values for the variables that satisfies all equations in the system.

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What does it mean for a system of equations to have no solution?

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It means the equations represent parallel lines that 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 any point on that line is a solution.

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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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How do you solve a system of equations using elimination?

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1. Align the equations. 2. Multiply equations if necessary to align coefficients. 3. Add or subtract equations to eliminate one variable.

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What is the graphical representation of a system of equations?

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The solutions are represented by the points where the graphs of the equations intersect.

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What is the y-coordinate of the solution to the system: x - 2y = 1 and x + 4y = 7?

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1

Front

Write a system of equations for the situation: Jose bought 236 paperclips and staples, with 27 less paperclips than staples.

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P + S = 236; P = S - 27.

Front

What does the graph of two intersecting lines represent?

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It represents a system of equations with a unique solution.