SOLUTION: Find all values of x satisfying the given condition. y1 = 5x+ 3, y2 = x+ 7, y3 = x, and the difference between 3 times y1 and 14 times y2 is 89 less than y3. Select the correc

Question 1153725: Find all values of x satisfying the given condition.
y1 = 5x+ 3, y2 = x+ 7, y3 = x, and the difference between 3 times y1 and 14 times y2 is 89 less than y3.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set Is . ()
B. There are infinitely many solutions.
C. There is no solution.
Answer by ikleyn(52792) (Show Source): You can put this solution on YOUR website!
.


First, you write this basic equation from the condition


    3*y1 - 14*y2 = y3 - 89.           (1)


Then you substitute given expressions for y1, y2 and y3 into this equation.  You get


    3*(5x+3) - 14*(x+7) = x - 89.     (2)


Next, you simplify the equation step by step


    15x + 9 - 14x - 98 = x - 89

    (15x - 14x) + (9 - 98) = x - 89

     x          + (-89)    = x - 89

     x - x                 = 89 - 89

     0                     = 0.


You get a true identity.  It means that equations (1) and/or (2) has INFINITELY MANY solutions.


Any value of x provides a valid solution.


The ANSWER is option B.

Solved, answered, explained and completed.

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