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 no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines.

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 solve a system of equations using 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 using elimination?

Back

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

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

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

Back

(3, 0)