Question

For what value of the constant a does the system of equations below have infinitely many solutions?

Answer 1

a = 8

Explanation:

For the 2 equations to have infinite solutions we require the solution to be in the form

0 = 0

Given

2x + 5y = - 8 → (1)

6x = 16 + a - 15y ( add 15y to both sides )

6x + 15y = 16 + a → (2)

Multiply (1) by - 3

- 6x - 15y = - 24 → (3)

Adding (2) and (3) term by term gives

0 + 0 = 16 + a - 24

For the right side to be zero , then

16 + a = 24 ( subtract 16 from both sides )

a = 8

Answer 2

1) Try a = 23/2. With this value, equation 1 multiplied by 2 is exactly the same as equation 2.

2) Try dividing 2005/3 + 2005/4 - 2005/6. Ignore the fractional parts.

3) If you are allowed to repeat the letters, then you should have: 3^3 = 27