Systems of Equations

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 eliminate a variable in a system of equations?

Back

To remove one variable by adding or subtracting equations, making it easier to solve for the remaining variable.

Front

What is the coefficient in an equation?

Back

The numerical factor that multiplies a variable, e.g., in 4x, 4 is the coefficient.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are true, the point is a solution.

Front

What is substitution in solving systems of equations?

Back

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

Front

What is the graphical representation of a system of equations?

Back

The point(s) where the graphs of the equations intersect represent the solution(s) of the system.

Front

What does it mean if two equations are parallel?

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They have the same slope but different y-intercepts, meaning they never intersect and have no solution.

Front

What is the solution to a system of equations?

Back

The values of the variables that satisfy all equations in the system.

Front

How can you check your solution for a system of equations?

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By substituting the solution back into the original equations to see if they hold true.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.