Systems Of Equations (fall24)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines or curves represented by the equations.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is an independent system of equations?

Back

A system that has exactly one solution, where the lines intersect at a single point.

Front

What is a dependent system of equations?

Back

A system that has infinitely many solutions, where the equations represent the same line.

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What is an inconsistent system of equations?

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A system that has no solution, where the equations represent parallel lines that never intersect.

Front

How do you find the x-value in a system of equations?

Back

By isolating x in one of the equations or using substitution or elimination methods.

Front

What is the first step in solving the system: y = 2x + 1 and y = 4x - 1?

Back

Set the two equations equal to each other: 2x + 1 = 4x - 1.