Systems of equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The solution is the point where the graphs of the equations intersect.

Front

What does it mean for a system of equations to be inconsistent?

Back

It means there is no solution; the equations represent parallel lines that never intersect.

Front

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

Back

It means there are infinitely many solutions; the equations represent the same line.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the first step in solving the system: x + 6y = 17 and 2x - 6y = 16?

Back

You can use either substitution or elimination; for elimination, you can add the two equations.

Front

What is the solution to the system: x + y = 10 and x - y = 2?

Back

(6, 4) is the solution.

Front

What is the solution to the system: 3x + 2y = 12 and 6x + 4y = 24?

Back

There are infinitely many solutions; the second equation is a multiple of the first.