Solving 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 for an ordered pair to be a solution to a system of equations?

Back

It means that the ordered pair makes all equations in the system true.

Front

How can you determine if a system of equations has no solution?

Back

If the lines represented by the equations are parallel, they do not intersect.

Front

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

Back

The point where the lines intersect on a graph.

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 substitution method in solving systems of equations?

Back

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

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you solve the system: 3x + 2y = 6 and x - y = 1?

Back

The solution is (2, 0).

Front

What is the first step in solving a system of equations using elimination?

Back

Align the equations so that like terms are in the same column.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.