Sorry, but I have a problem where I must add two terms like this in a simultaneous equation:
2x + 4y = 32
2x - 3y = 11
I want to add the terms 4y and 3y, because they are different signs. If I do it I get y. I checked my answer and my answer was wrong. It will only be correct if the sum of the two terms are 7y. And in the book, there was a solved example that was solved this way with the signs ignored and they were just added.
I think the sum must be y because 4y + -3y = 4y - 3y = y. Why is that?
Sorry, I am studying for my exam tomorrow.
You need to subract, rather than add to get rid of $\space x.\space $ In general, you want to add/subtract terms or multiples of terms so that one-or-more variables cancel.
\begin{align*} 2x + &4y = 32\\ -(2x - &3y = 11)\\ &\overline{7y=21}\\ \implies &\space \space y=3 \end{align*}
\begin{align*} \\ 2x + 4(3) &= 32\\ \implies 2x &=32-12\\ \implies x&=10\\ \\ 2x - 3(3) &= 11\\ \implies 2x &= 11 +9\\ \implies x&=10\\ \end{align*}