How do I solve this? What are the steps?

Solve the following systems of equations. In other words, find values of a and b that make each system true. Write your answer as an ordered pair (a,b).

3= a(b)⁰
75= a(b)²

1 Answer
Douglas K. · Jordan N.
Feb 5, 2018

Use the fact that any number raised to the 0 power is 1, to solve the first equation for the value of 'a'
Substitute the value of 'a' into the second equation and then solve b.

Explanation:

Given:

#3= a(b)^0#
#75= a(b)^2#

We know that #(b)^0 = 1#, therefore the first equation becomes:

#3= a(1)#

Solving for a:

#a=3#

Substituting into the second equation:

#75 = 3b^2#

Divide both sides by 3:

#b^2 = 25#

Use the square root on both sides. Remember that the square root has a negative and a positive value.

#b = -5 or b = 5#

There are two possible solutions #(3,5)# or #(3,-5)# and we are not given enough information to tell which is correct.

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