Answer :
Final answer:
The equations that have infinitely many solutions are options a) -75 × 57 = -75 × 57 and d) 57 × 57 = -75 × -75, because the expressions on both sides of these equations are identical, hence they hold true for all values.
Explanation:
In the field of Mathematics, an equation has infinitely many solutions if the left side of the equation is identical to the right side of the equation. This means that they are identical expressions and thus hold true for all values of the variable involved.
From the given options, options a) -75 × 57 = -75 × 57 and d) 57 × 57 = -75 × -75 have infinitely many solutions. This is because in both equations, the expressions on both sides of the equality sign are identical. Therefore, they hold true for all values, which means they have infinitely many solutions.
If for instance, you were to replace any variable in option a) with any number, it will hold true because -75 times 57 is always equal to -75 times 57, and similarly for option d).
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