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 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 the variable 'x' typically represent in a system of equations?

Back

In a system of equations, 'x' often represents one of the unknown quantities that you are trying to solve for.

Front

What does the variable 'y' typically represent in a system of equations?

Back

In a system of equations, 'y' often represents another unknown quantity that is related to 'x'.

Front

What is the purpose of solving a system of equations?

Back

The purpose is to find the values of the variables that make all equations in the system true.

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 does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect, indicating that there are no values for the variables that satisfy all equations.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and any point on that line is a solution to the system.

Front

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

Back

You can substitute the values of the variables back into the original equations to see if they hold true.