System 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 solution?

Back

It means there is at least 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 graphical representation consists of lines or curves that represent each equation.

Front

What does it mean if two lines intersect on a graph?

Back

It means the system of equations has a unique solution.

Front

What does it mean if two lines are parallel?

Back

It means the system of equations has no solution.

Front

What does it mean if two lines are the same?

Back

It means the system of equations has infinitely many solutions.

Front

How do you solve a system of equations by substitution?

Back

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

Front

How do you solve a system of equations by elimination?

Back

You add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the solution to the system: x - y = 6 and y = 2x - 5?

Back

(-1, -7) is the solution.

Front

What is the solution to the system: 5x + 6y = -10 and 3x - 2y = -6?

Back

(-2, 0) is the solution.