# Thread: [SOLVED] Solving for two unknowns

1. ## [SOLVED] Solving for two unknowns

For the love of God, will someone please solve the following problem and then kindly explain to me how they did it? If you do so and you live in Springfield, Ohio, I will buy you something under $10. K? 7x-5y=13 2x-7y=26 9x-12y=? 2. Hello, I'll steal your money, better way to get something Just add term by term the two equalities. (7x-5y)+(2x-7y) = 9x-12y But 7x-5y is ... ? And 2x-7y... ? 3. Originally Posted by Solomoreno For the love of God, will someone please solve the following problem and then kindly explain to me how they did it? If you do so and you live in Springfield, Ohio, I will buy you something under$10. K?

7x-5y=13
2x-7y=26
9x-12y=?
Notice that $\displaystyle 7x+2x=9x$ and $\displaystyle -5y-7y=-12y$. The top two equations add up to equal to the third equation. Therefore $\displaystyle ? = 13 + 26 \Rightarrow 39$

4. Originally Posted by Solomoreno
For the love of God, will someone please solve the following problem and then kindly explain to me how they did it? If you do so and you live in Springfield, Ohio, I will buy you something under $10. K? 7x-5y=13 2x-7y=26 9x-12y=? It looks to me as if you have started to solve$\displaystyle \left|\begin{array}{lcr}7x-5y&=&13\\2x-7y&=&26 \end{array}\right.$... If so multiply the first equation by (-2) and the second one by (+7). That is necessary to get coefficients of x which have the same value but opposite signs:$\displaystyle \left|\begin{array}{lcr}-14x+10y&=&-26\\14x-49y&=&182 \end{array}\right.$... Now add columnwise(?):$\displaystyle -39y = 156~\implies~\boxed{y = -4}\$ ... Plug in this value into one of the original equations (it doesn't matter which one) and solve for x.

I've got x = -1