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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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What does it mean to solve a system of equations by elimination?

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Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

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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 is the elimination method in solving equations?

Back

The elimination method involves manipulating equations to eliminate one variable, allowing for the straightforward solving of the remaining variable.

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What is the significance of the coefficients in a system of equations?

Back

Coefficients represent the relationship between variables in an equation. They determine the slope and position of the lines represented by the equations.

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

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Substitute the solution back into the original equations to verify that both equations hold true.

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What is the graphical interpretation of a system of equations?

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The graphical interpretation involves plotting the equations on a coordinate plane; the solution is where the lines intersect.

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

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

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

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If two lines coincide, it means there are infinitely many solutions, as every point on the line is a solution to the system.

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How do you form a system of equations from a real-world scenario?

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Identify the quantities involved, assign variables, and create equations based on the relationships and totals described in the scenario.