Understanding Solutions to Linear Equations

The video tutorial covers Unit 4, Lesson 2 on the number of solutions to linear equations. It explains the conditions for one solution, no solution, and infinite solutions. The lesson includes graphical and algebraic methods to find solutions, with examples and practice problems sourced from Khan Academy.

What condition must be met for two linear equations to have exactly one solution?

• They must be identical.

• They must be parallel.

• They must have different slopes.

• They must have the same slope and y-intercept.

What is the slope of a line that rises 1 and runs 1?

• 0

• 1

• -1

• Undefined

When do two linear equations have no solution?

• When they have the same slope but different y-intercepts.

• When they have different slopes.

• When they are identical.

• When they intersect at one point.

How can you determine if two lines are parallel?

• They are identical.

• They intersect at one point.

• They have the same slope but different y-intercepts.

• They have different slopes.

What does it mean when two linear equations have infinite solutions?

• They intersect at one point.

• They are parallel.

• They are the same line.

• They have different slopes.

What is the result when two lines have the same slope and y-intercept?

• Infinite solutions

• No solution

• One solution

• Two solutions

Which method can be used to find the exact point of intersection for two lines?

• Elimination

• Graphing

• Substitution

• All of the above

What is the algebraic method used to solve for x in a system of equations?

• Substitution

• None of the above

• Elimination

• Graphing

What is the significance of the y-intercept in determining the number of solutions?

• It helps identify if lines are parallel.

• It is not important.

• It determines the slope.

• It shows where the line crosses the x-axis.

What happens when you multiply both sides of an equation by the same number?

• The equation becomes unbalanced.

• The equation remains balanced.

• The equation has no solution.

• The equation has infinite solutions.