Systems and Word Problems

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution to the system is the point(s) where the equations intersect.

Front

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 constraints of the problem.

Front

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 you are trying to solve for.

Front

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' through the equations.

Front

What is substitution in the context of solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into another equation.

Front

What is the elimination method in solving systems of equations?

Back

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

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What does it mean for a system of equations to be consistent?

Back

A consistent system of equations has at least one solution, meaning the lines represented by the equations intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system of equations has no solutions, meaning the lines represented by the equations are parallel and never intersect.

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

Back

The graphical representation of a system of linear equations consists of lines on a coordinate plane, where the intersection points represent the solutions.

Front

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

Back

To check if a solution is correct, substitute the values of the variables back into the original equations to see if they satisfy all equations.