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 represented by 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 represented by the equations are the same line.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

What is the slope-intercept form of a line?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the intersection of two lines given by equations?

Back

Set the equations equal to each other and solve for the variable.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

Front

What is the substitution method in 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 in solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve.