Solving 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 two equations to intersect on a graph?

Back

It means they have a common solution (x, y) that satisfies both equations.

Front

How do you solve a system of equations by substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

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

Back

(3, 0)

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable.

Front

What is the solution to the system: 4x + 9y = 28 and -4x - y = -28?

Back

(7, 0)

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.