Graphing Systems of Equations HW

Front

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

Back

The lines representing the equations are parallel and will never intersect.

Front

What does it indicate if two lines in a system of equations are the same line?

Back

It means the system has infinitely many solutions.

Front

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

Back

You graph both equations on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the graphical representation of a system of equations with exactly one solution?

Back

The two lines intersect at a single point.

Front

What happens when you graph the same linear equation twice?

Back

You will have infinite solutions since both lines overlap.

Front

What is the solution to the system of equations y = 6x - 4 and y = -x + 3?

Back

The solution is the point (1, 2).

Front

What is the significance of the intersection point of two lines in a system of equations?

Back

It represents the solution to the system, where both equations are satisfied.

Front

How can you tell if a system of equations has no solution by looking at their slopes?

Back

If the slopes of the two lines are equal but the y-intercepts are different, the system has no solution.

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

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution.