Systems of Linear Equations

Front

What is a system of linear equations?

Back

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

Front

What does it mean if a system has one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean if a system has no solution?

Back

The lines are parallel and never intersect.

Front

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

Back

The lines are the same, meaning they overlap completely.

Front

How do you solve a system of equations graphically?

Back

By plotting the equations on a graph and finding the intersection point.

Front

What is the substitution method?

Back

A method where you solve one equation for a variable and substitute it into the other equation.

Front

What is the elimination method?

Back

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

Front

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

Back

(-9, 3)

Front

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

Back

(3, 0)

Front

What is the solution to the system: y = 4x + 1 and 3x + 2y = 13?

Back

(1, 5)