Solving 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 for a system of equations to have a solution?

Back

It means there is at least one set of values for the variables that satisfies all equations in the system.

Front

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

Back

The point where the graphs of the equations intersect.

Front

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

Back

It means the system has no solution because the lines never intersect.

Front

How can you determine the solution of a system of equations by graphing?

Back

By plotting the equations on a graph and identifying the intersection point.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What does it indicate if the lines of a system of equations intersect at one point?

Back

The system has exactly one solution.

Front

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

Back

No solution (the lines are parallel).

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

2 (the coefficient of x).

Front

What is the y-intercept of the equation y = -x + 5?

Back

5 (the constant term).