Systems Of Equations

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

The lines are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The lines coincide, meaning they are the same line.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

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.

Front

How do you find the solution to a system of equations graphically?

Back

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

Front

What is the substitution method for solving systems of equations?

Back

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

Front

What is the elimination method for solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve.

Front

What is the significance of the determinant in a system of equations?

Back

A non-zero determinant indicates a unique solution; a zero determinant indicates no or infinitely many solutions.