Systems of Linear Equations (Two Variables)

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 for a solution to a system of linear equations?

Back

A solution must make all equations in the system true.

Front

How is a solution to a system of linear equations represented?

Back

As an ordered pair (x, y).

Front

What is the graphical representation of a system of linear equations?

Back

The intersection point(s) of the lines representing the equations.

Front

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

Back

The lines are parallel and do not intersect.

Front

What does it mean if a system of linear equations has infinite solutions?

Back

The lines are coincident, meaning they lie on top of each other.

Front

How can you determine if a system of linear equations has one solution?

Back

The lines intersect at exactly one point.

Front

What is the substitution method in solving systems of equations?

Back

Solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.