Types of Solutions from Systems of Equations

Front

What are the types of solutions for a system of equations?

Back

1. No Solution 2. One Solution 3. Infinitely Many Solutions

Front

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

Back

The equations represent parallel lines that never intersect.

Front

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

Back

The equations represent lines that intersect at exactly one point.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How can you identify a system of equations with no solution graphically?

Back

The graph will show parallel lines.

Front

How can you identify a system of equations with one solution graphically?

Back

The graph will show two lines that intersect at a single point.

Front

How can you identify a system of equations with infinitely many solutions graphically?

Back

The graph will show two overlapping lines.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

What is the graphical representation of the equation y = -x + 3?

Back

A straight line with a slope of -1 and a y-intercept of 3.

Front

If two lines are parallel, what can be said about their slopes?

Back

The slopes of parallel lines are equal.