Question

21x + 14 = 7(3x + a) In the equation above, a is a constant. For what value of a does the equation have an infinite number of solutions? If a + b = 6 and a - b = 4, What is the value of 2a + 3b?

Answer 1

1. a = 2
2. 2a+3b = 13

Explanation:

1. For there to be an infinite number of solutions, both sides of the equation need to have the same values.

21x +14 = 21x +7a

That is, 7a must be 14. For a = 2, there are infinite solutions.

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2. To find the value of b, we can substitute for a in the second equation using the value of a we find from the first equation:

a = 6 -b . . . . . . . expression for a

(6 -b) -b = 4 . . . . substituted into the second equation

2 -2b = 0 . . . . . . subtract 4

1 - b = 0 . . . . . . . divide by 2

b = 1 . . . . . . . . . . add b

We want 2a +3b = 2(a+b) +b = 2(6) +1 = 13. The value of 2a +3b is 13.