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)

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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

2 5/8 is the final answer! : )

8

step-by-step explanation: