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 graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and 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 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.

Front

How do you write an equation from a word problem?

Back

Identify the variables, translate the relationships and conditions into mathematical expressions, and form an equation.

Front

What is the cost equation for Joe's coffee and doughnuts?

Back

10c + 5d = 16.50 and 5c + 10d = 14.25, where c is the cost of coffee and d is the cost of doughnuts.