Question

1) Multiply the first equation by 7 and multiply the second equation by -7 to eliminate the x variable:
7(7x+3y) = 7(-25)
-7(-7x+9y) = -7(-47)

why is the first 7 positive and the second one is negative

Answer 1

To eliminate the x variable, we need to create opposing terms (one positive and one negative) so that when we add the two equations together, the x term cancels out. In this case, we multiply the first equation by 7 to get a positive 7x term, and we multiply the second equation by -7 to get a negative -7x term. By doing this, when we add the two equations together, the x terms will cancel each other out.