Elimination Addition Practice

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, allowing for the solution of the remaining variable.

Front

What is the addition method in solving systems of equations?

Back

The addition method, also known as the elimination method, involves manipulating equations to add them together to eliminate one variable.

Front

How do you determine if a system of equations has no solutions?

Back

A system of equations has no solutions if the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts.

Front

What does it mean for two equations to be dependent?

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Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

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

How can you identify the best method to solve a system of equations?

Back

The best method can be identified based on the structure of the equations; for example, if one equation is already solved for a variable, substitution may be easiest.

Front

What is the graphical interpretation of a system of equations with one solution?

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A system of equations with one solution is represented graphically by two lines that intersect at a single point.

Front

What is the significance of the coefficients in a system of linear equations?

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The coefficients determine the slope and position of the lines represented by the equations, affecting whether they intersect, are parallel, or are the same line.

Front

How do you solve a system of equations using the elimination method?

Back

To solve using the elimination method, align the equations, multiply if necessary to match coefficients, and then add or subtract the equations to eliminate one variable.

Front

What is the first step in using the substitution method?

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The first step in the substitution method is to solve one of the equations for one variable in terms of the other variable.