Solve System of Equations by Graphing

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

It means there is no solution to the system because the lines never intersect.

Front

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

Back

It means there are infinitely many solutions because the lines are the same.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the two lines intersect on a graph.

Front

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

Back

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

Front

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

Back

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

Front

What does the slope of a line represent?

Back

The rate of change of y with respect to x; it indicates how steep the line is.

Front

How do you find the y-intercept of a line from its equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is the solution to the system of equations y = 2x + 3 and y = 2x - 1?

Back

No solution, as the lines are parallel.

Front

What is the solution to the system of equations y = x + 1 and y = -x + 3?

Back

(1, 2), as the lines intersect at this point.