Systems and Word Problems

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

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

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

It means the lines represented by the equations are parallel and do not intersect.

Front

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

Back

Coefficients determine the slope and position of the lines represented by the equations.

Front

How do you determine which variable to eliminate in the elimination method?

Back

Choose the variable that can be easily eliminated by adding or subtracting the equations.

Front

What is a word problem in the context of systems of equations?

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A real-world scenario that can be modeled using a system of linear equations.

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, write equations based on the relationships described, and ensure they reflect the problem's constraints.

Front

What is the graphical interpretation of a system of linear equations?

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The solutions to the system are the points where the lines intersect on a graph.

Front

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, and every point on that line is a solution.