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 if a system of equations has one solution?

Back

The lines intersect at exactly one point, representing a unique solution for the variables.

Front

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

Back

The lines are parallel and never intersect, indicating that there is no set of values that satisfies both equations.

Front

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

Back

The lines coincide, meaning they are the same line and have an infinite number of intersection points.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel 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

Plot both equations on the same graph and identify the point(s) where they intersect.

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 for the other.

Front

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

Back

Coefficients determine the slope and position of the lines represented by the equations.