System of Equations (Set Equal)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means the graphs of 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 graphs of the equations are parallel and 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 they intersect at every point on that line.

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 graphical representation consists of lines on a coordinate plane, where their intersections represent solutions.

Front

Solve the system: 2x + 3y = 6 and x - y = 1.

Back

(3,0)

Front

Solve the system: y = 3x + 4 and y = -2x + 1.

Back

(-1,1)

Front

What is the slope of the line represented by the equation y = mx + b?

Back

The slope is 'm', which indicates the steepness and direction of the line.