Solving 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 a unique solution?

Back

It means the equations intersect at exactly one point.

Front

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

Back

It means the equations represent parallel lines that never intersect.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How do you solve a system of equations by substitution?

Back

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

Front

How do you solve a system of equations by elimination?

Back

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

Front

What is the graphical representation of a system of equations?

Back

The solutions are represented by the points where the graphs of the equations intersect.

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

What is the point of intersection of two lines?

Back

The point where the two lines cross, representing the solution to the system of equations.

Front

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

Back

They determine the slope and position of the lines in the graph.