Solving Systems

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 has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean if a system has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How do you solve a system of equations by substitution?

Back

Solve one equation for one variable and 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 solution is represented by the point(s) where the graphs of the equations intersect.

Front

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

Back

(1, 3)

Front

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

Back

(3, 0)

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

3, which indicates the line rises 3 units for every 1 unit it runs to the right.