Lesson 19 Formulating a System of Equations

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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.

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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 all equations are aligned with the problem's context.

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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 make all equations true at the same time.

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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(s).

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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.

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What is a consistent system of equations?

Back

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

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What is an inconsistent system of equations?

Back

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

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What is a dependent system of equations?

Back

A dependent system 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

Substitute the values of the variables back into the original equations to see if they satisfy all equations.

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves plotting each equation on a graph and identifying the point(s) where the lines intersect.