Intro to 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 two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

Front

What does it mean if two lines are the same in a system of equations?

Back

There are infinitely many solutions because every point on the line is a solution.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are true, it is a solution.

Front

What is the graphical representation of a system of equations?

Back

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

Front

What is the solution to a system of equations represented graphically?

Back

The point(s) where the lines intersect.

Front

If a system of equations has one solution, what does this indicate about the lines?

Back

The lines intersect at exactly one point.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line.

Front

What does it mean if a system of equations has no solution?

Back

The lines are parallel and will never intersect.

Front

How do you find the number of solutions in a system of equations?

Back

Analyze the slopes and y-intercepts of the lines.