Setting up Systems of Equations

Front

What is a system of equations?

Back

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

Front

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 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

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

Back

Identify the variables, translate the relationships and conditions into equations, and set them equal to each other.

Front

What is the graphical method for solving systems of equations?

Back

Plotting the equations on a graph and finding the point(s) where they intersect, which represents the solution.

Front

What does it mean if two lines are parallel in a system of equations?

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The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide in a system of equations?

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The system has infinitely many solutions because the equations represent the same line.

Front

What is the importance 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 check the solution of a system of equations?

Back

Substitute the values of the variables back into the original equations to verify they hold true.