Graphing systems of equations

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 are the same in a system of equations?

Back

It means there are infinitely many solutions because every point on the line is a solution.

Front

How do you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

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

Back

No Solution (the lines are parallel).

Front

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

Back

(1, 3) (the lines intersect at this point).

Front

What does it mean if a system of equations has one solution?

Back

It means the lines intersect at exactly one point.

Front

What is the graphical representation of the equation y=3x+2?

Back

A straight line with a slope of 3 and a y-intercept of 2.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

What is the slope of the line represented by the equation y=4x-1?

Back

4 (the coefficient of x represents the slope).