Solving Systems by Graphing

Front

What is the solution to the system of equations represented by the intersection of two lines?

Back

The solution is the point where the two lines intersect, representing the values of the variables that satisfy both equations.

Front

How do you solve a system of equations by graphing?

Back

To solve by graphing, plot both equations on the same coordinate plane and identify the point(s) where they intersect.

Front

What does it mean if two lines are parallel when graphing a system of equations?

Back

If two lines are parallel, it means they have no points in common, indicating that the system has no solution.

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of two or more lines on a coordinate plane, each representing an equation.

Front

What is the significance of the point (1, -1) in a system of equations?

Back

The point (1, -1) is a solution to the system if it satisfies both equations.

Front

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

Back

Count the number of intersection points: no intersection means no solution, one intersection means one solution, and overlapping lines mean infinitely many solutions.

Front

What is the solution to the system of equations if the lines intersect at (-2, -3)?

Back

The solution to the system is (-2, -3), which satisfies both equations.

Front

What happens when you graph the same equation twice?

Back

Graphing the same equation twice results in a single line, indicating infinitely many solutions.

Front

What does 'no solution' mean in the context of a system of equations?

Back

'No solution' means that the equations represent lines that do not intersect at any point.