Systems of Equations Warm Up

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 to the system is the set of values that satisfy all equations simultaneously.

Front

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

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Front

What does it mean for two variables to be dependent in a system of equations?

Back

Two variables are dependent if one variable can be expressed as a function of the other, meaning they do not have unique 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

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where the graphs intersect, which represent the solution(s).

Front

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

Back

Coefficients represent the relationship between the variables in the equations. They determine the slope and position of the lines when graphed.

Front

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

Back

Substitute the solution values back into the original equations to verify that both equations are satisfied.

Front

What is a consistent system of equations?

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A consistent system has at least one solution, meaning the equations intersect at one or more points.

Front

What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.