Understanding Solutions for Systems of Equations

The video tutorial explains three types of solutions for a system of equations: one solution, no solution, and infinite solutions. One solution occurs when an ordered pair satisfies both equations. No solution arises when lines are parallel and never intersect, having the same slope but different y-intercepts. Infinite solutions occur when lines coincide, sharing both slope and y-intercept. The video concludes with a message promoting kindness.

What happens when a system of equations has exactly one solution?

• The lines never intersect.

• The lines are parallel.

• The lines are the same.

• The lines intersect at one point.

In a system with no solution, what is true about the lines?

• They are the same line.

• They intersect at one point.

• They have different slopes.

• They are parallel with different y-intercepts.

What is the relationship between the slopes of two lines in a system with no solution?

• The slopes are different.

• The slopes are the same.

• One slope is double the other.

• The slopes are negative reciprocals.

When do two lines in a system have an infinite number of solutions?

• When they are the same line.

• When they have different slopes.

• When they intersect at one point.

• When they are parallel.

What must be true about the y-intercepts of two lines that have infinite solutions?

• They must be different.

• They must be positive.

• They must be the same.

• One must be zero.