Determining Solutions for Systems of Equations

What form of a line is used to determine the number of solutions in a system of equations?

• Slope-intercept form

• Point-slope form

• Standard form

• Quadratic form

If two lines have the same slope but different y-intercepts, what can be said about their solutions?

• They intersect at two points

• They have no solution

• They have one solution

• They have infinitely many solutions

What is the result when two lines have different slopes?

• Parallel lines

• No solution

• One solution

• Infinitely many solutions

In Example 1, what is the number of solutions for the system y = -2x + 4 and y = 3/4x + 2?

• One solution

• Cannot be determined

• Infinitely many solutions

• No solution

In Example 2, what is the number of solutions for the system y = 2/3x + 3 and 3y = 2x + 15?

• Cannot be determined

• One solution

• No solution

• Infinitely many solutions

In Example 3, what is the number of solutions for the system y = 3/4x and 3x - 4y = 0?

• Infinitely many solutions

• One solution

• No solution

• Cannot be determined

If two lines have the same slope and the same y-intercept, what can be said about their solutions?

• They intersect at two points

• They have no solution

• They have one solution

• They have infinitely many solutions

What is the y-intercept of the line passing through the points (0, 4) and (3, 2)?

• 2

• 3

• 0

• 4

What is the slope of the line passing through the points (3, -3) and (9, -7)?

• -2/3

• 2/3

• -4/6

• 4/6

In Example 4, what is the number of solutions for the lines passing through (0, 4) and (3, 2) and the lines passing through (3, -3) and (9, -7)?

• Infinitely many solutions

• One solution

• No solution

• Cannot be determined