12/10 bell-ringer

Front

What is a system of equations?

Back

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

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What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the Elimination Method?

Back

The Elimination Method is a technique for solving systems of equations by adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

How do you identify the solution of a system of equations graphically?

Back

The solution of a system of equations can be identified graphically as the point where the graphs of the equations intersect.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

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 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 equations represent parallel lines that never intersect.

Front

What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.

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How can you check if your solution to a system of equations is correct?

Back

You can check your solution by substituting the values back into the original equations to see if they hold true.

Front

What is the first step in solving a system of equations using the Elimination Method?

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The first step is to align the equations and manipulate them (if necessary) so that adding or subtracting them will eliminate one variable.