151k views
1 vote
Substitute -3 for a and 8 for b in the given equations. Then, tell whether each equation is true or false.

The equation 5x - 7 (x - 1) = ax + b has excalty one solution (True or False)
The equation 3 (x - 5) - 7 = ax + b has no solution (True or False)
The equation 2 - 7x + 3 + 4x = ax + b has no solution (True or False)
The equation -3 (x - 3) - 1 = ax + b has infinitely many solutions (True or False)
The equation -5x + 2 + 2x + 4 = ax + b has infinitely many solutions (True or False)

User Adjit
by
8.7k points

1 Answer

2 votes

Answer:

see below

Explanation:

The equation 5x - 7 (x - 1) = ax + b has exactly one solution (True or False)

Distribute the -7 and substitute a and b

5x - 7x+7 = -3x+8

-2x+7 = -3x+8

This has one solution because they are not the same line or parallel lines.

True


The equation 3 (x - 5) - 7 = ax + b has no solution (True or False)

Distribute the 3 and substitute a and b

3x-15 -7 = -3x+8

3x-22 = -3x+8

The slopes are not the same so they are not parallel lines. It has one solution.

False


The equation 2 - 7x + 3 + 4x = ax + b has no solution (True or False)

Substitute in a and b

2 - 7x + 3 + 4x = -3x + 8

Combine like terms

5 -3x = -3x+8

The slopes are the same but the y intercepts are different. The lines will never intersect. They have no solutions

True


The equation -3 (x - 3) - 1 = ax + b has infinitely many solutions (True or False)

Distribute the -3 and substitute a and b

-3 (x - 3) - 1 = -3x + 8

-3x +9 -1 = -3x +8

-3x+8 = -3x+8

This is the same line so it has infinite solutions

True


The equation -5x + 2 + 2x + 4 = ax + b has infinitely many solutions (True or False)

Substitute in a and b

-5x + 2 + 2x + 4 = -3x + 8

-3x+6 = -3x+8

The slopes are the same but the y intercepts are different. These are parallel lines so they do not intersect. There are no solutions

False

User David Nouls
by
7.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories