Systems of 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: 2x + 3y = 12 and x - y = 2?

Back

(2, 3)

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

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 does it mean if two lines intersect at a point in a system of equations?

Back

The system has one unique solution at the point of intersection.

Front

Solve the system of equations: 3x + 4y = 10 and 6x - 2y = 12.

Back

(2, 1)

Front

What is a system of equations?

Back

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

Front

If the equations in a system are identical, what can be said about the solutions?

Back

There are infinitely many solutions.

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that value into the other equation.

Front

What does it indicate if the lines of a system of equations are skew?

Back

The system has no solution, as skew lines do not intersect.