Systems of Equations- Graphing & Word Problems

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

What does it mean for a system of equations to have no solution?

Back

A system has no solution when the lines represented by the equations are parallel and never intersect.

Front

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

Back

A system has one solution when the lines represented by the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system has infinitely many solutions when the equations represent the same line, meaning they overlap completely.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept and slope, plot the y-intercept on the graph, and use the slope to find another point.

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

How can you determine the point of intersection of two lines graphically?

Back

The point of intersection is where the two lines cross on the graph. This point represents the solution to the system of equations.

Front

What is a word problem in the context of systems of equations?

Back

A word problem is a real-life scenario that can be modeled using a system of equations to find unknown values.

Front

How do you set up a system of equations from a word problem?

Back

Identify the variables, translate the relationships and conditions into equations, and write them as a system.

Front

What is the importance of finding the point of intersection in a word problem?

Back

Finding the point of intersection helps determine the values that satisfy all conditions of the problem.