System of Equations Word Problems

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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 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?

Back

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 the variable 'x' typically represent in a system of equations?

Back

In a system of equations, 'x' usually represents one of the unknown quantities that need to be solved for.

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What does the variable 'y' typically represent in a system of equations?

Back

In a system of equations, 'y' usually represents another unknown quantity that is related to 'x'.

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

Back

Substitute the solution values back into the original equations. If both equations are satisfied, the solution is correct.

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What is the graphical representation of a system of equations?

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The graphical representation consists of the lines of each equation plotted on a coordinate plane. The point of intersection represents the solution.

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What does it mean if two lines in a system of equations are parallel?

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If two lines are parallel, it means there is no solution to the system, as the equations represent lines that never intersect.

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What does it mean if two lines in a system of equations coincide?

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If two lines coincide, it means there are infinitely many solutions, as the equations represent the same line.

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How do you solve a system of equations using substitution?

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Solve one equation for one variable, then substitute that expression into the other equation to find the value of the second variable.

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How do you solve a system of equations using elimination?

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Add or subtract the equations to eliminate one variable, making it easier to solve for the remaining variable.