Systems of Linear Equations

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 linear equations?

Back

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

Front

What is substitution in the context of solving linear 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 method of solving a system of linear equations?

Back

Plotting the equations on a graph and identifying the point(s) where they intersect.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How can you determine the number of solutions in a system of linear equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

What is the slope-intercept form of a linear equation?

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y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the elimination method for solving systems of equations?

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A method where you add or subtract equations to eliminate one variable.

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What is a consistent system of equations?

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A system that has at least one solution.