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)

see below

Step-by-step 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