Solve Systems Of Equations By Inspection

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

They have no points in common, resulting in no solution.

Front

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

Back

They have exactly one point in common, resulting in one solution.

Front

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

Back

They have infinitely many points in common, resulting in infinitely many solutions.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the intersection of lines on a coordinate plane.

Front

If the equations y = 2x + 5 and y = 2x - 3 are graphed, what is the solution?

Back

No solution, as the lines are parallel.

Front

If the equations y = 2x + 4 and y = 2x + 6 are graphed, what is the solution?

Back

Infinitely many solutions, as the lines are parallel.

Front

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

Back

1 solution, as the lines intersect at one point.

Front

What is the solution to the system of equations y = 3x + 1 and y = -3x + 7?

Back

1 solution, as the lines intersect at one point.

Front

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

Back

If the slopes are equal, the lines are parallel; if they are different, the lines will intersect.