Systems of Linear Equations

Front

What does the graph of a system of equations with no solution look like?

Back

The graph consists of parallel lines.

Front

What is the solution to the system of equations: y = 2x + 1 and y = 4x - 1?

Back

(1, 3)

Front

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

Back

It means that the equations represent the same line.

Front

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

Back

If the lines are parallel, they will never intersect.

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Front

What is the definition of 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 of equations has one solution?

Back

The lines intersect at exactly one point.

Front

How do you solve a system of equations using substitution?

Back

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

Front

What is the graphical representation of a system with infinitely many solutions?

Back

The graph consists of the same line drawn multiple times.

Front

What is the solution to the system of equations: x + y = 5 and x - y = 1?

Back

(3, 2)