Writing Systems of Equations

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 set of values that satisfy all equations in the system.

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 to solve a system of equations graphically?

Back

To solve a system of equations graphically means to plot the equations on a graph and find the point(s) where they intersect, which represents the solution.

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 a consistent system of equations?

Back

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

Front

What is an inconsistent system of equations?

Back

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

Front

What is a dependent system of equations?

Back

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

Front

How do you check the solution of a system of equations?

Back

To check the solution, substitute the values of the variables back into the original equations to see if they hold true.

Front

What is the importance of defining variables in a word problem?

Back

Defining variables helps clarify what each variable represents, making it easier to translate the problem into equations.