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 represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and set them equal to each other based on the problem's context.

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What does it mean for two equations to have one solution?

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It means that the lines represented by the equations intersect at exactly one point, indicating a unique solution for the variables.

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What does it mean for two equations to have no solution?

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It means that the lines represented by the equations are parallel and never intersect, indicating that there is no set of values that satisfies both equations.

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What does it mean for two equations to have infinitely many solutions?

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It means that the lines represented by the equations coincide, or are the same line, indicating that there are an infinite number of points that satisfy both equations.

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How do you find the cost of items in a word problem involving equations?

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Set up equations based on the total cost and the number of items sold, then solve the system of equations to find the individual costs.

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

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The first step is to write the equations in a standard form, if necessary, and then decide on a method to solve them (substitution, elimination, or graphing).

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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 variable.

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How can you check the solution of a system of equations?

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Substitute the values of the variables back into the original equations to verify that both equations are satisfied.