True
Because a negative square root is an i
The slope is -2.
The slope is the rise over the run. Because the line goes down from left to right, it makes the value negative. For every one the it moves to the right, the line goes down two units.
so first off, let's simplify both equations, starting off by multiplying both sides by the LCD of all fractions, to do away with the denominators.
![\bf \cfrac{10(x-y)-4(1-x)}{3}=y\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{10(x-y)-4(1-x)=3y} \\\\\\ 10x-10y-4+4x=3y\implies \boxed{14x-13y=4} \\\\[-0.35em] ~\dotfill\\\\ 7+x-\cfrac{x-3y}{4}=2x-\cfrac{y+5}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( 7+x-\cfrac{x-3y}{4} \right)=12\left( 2x-\cfrac{y+5}{3} \right)} \\\\\\ 84+12x-3(x-3y)=24x-4(y+5) \\\\\\ 84+12x-3x+9y=24x-4y-20\implies \boxed{-15x+13y=-124}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B10%28x-y%29-4%281-x%29%7D%7B3%7D%3Dy%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B3%7D%7D%7B10%28x-y%29-4%281-x%29%3D3y%7D%20%5C%5C%5C%5C%5C%5C%2010x-10y-4%2B4x%3D3y%5Cimplies%20%5Cboxed%7B14x-13y%3D4%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%207%2Bx-%5Ccfrac%7Bx-3y%7D%7B4%7D%3D2x-%5Ccfrac%7By%2B5%7D%7B3%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B12%7D%7D%7B12%5Cleft%28%207%2Bx-%5Ccfrac%7Bx-3y%7D%7B4%7D%20%5Cright%29%3D12%5Cleft%28%202x-%5Ccfrac%7By%2B5%7D%7B3%7D%20%5Cright%29%7D%20%5C%5C%5C%5C%5C%5C%2084%2B12x-3%28x-3y%29%3D24x-4%28y%2B5%29%20%5C%5C%5C%5C%5C%5C%2084%2B12x-3x%2B9y%3D24x-4y-20%5Cimplies%20%5Cboxed%7B-15x%2B13y%3D-124%7D)
now, let's do some elimination on those two simplified equations.
![\bf \begin{array}{cllcl} 14x&-13y&=&4\\ -15x&+13y&=&-124\\\cline{1-4} -x&&=&-120 \end{array}~\hfill x=\cfrac{-120}{-1}\implies \blacktriangleright x=120 \blacktriangleleft \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{14(120)-13y=4}\implies 1680-13y=4\implies 1680-4=13y \\\\\\ 1676=13y\implies \blacktriangleright \cfrac{1676}{13}=y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( 120~,~\frac{1676}{13} \right)~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bcllcl%7D%2014x%26-13y%26%3D%264%5C%5C%20-15x%26%2B13y%26%3D%26-124%5C%5C%5Ccline%7B1-4%7D%20-x%26%26%3D%26-120%20%5Cend%7Barray%7D~%5Chfill%20x%3D%5Ccfrac%7B-120%7D%7B-1%7D%5Cimplies%20%5Cblacktriangleright%20x%3D120%20%5Cblacktriangleleft%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsubstituting%20on%20the%201st%20equation%7D%7D%7B14%28120%29-13y%3D4%7D%5Cimplies%201680-13y%3D4%5Cimplies%201680-4%3D13y%20%5C%5C%5C%5C%5C%5C%201676%3D13y%5Cimplies%20%5Cblacktriangleright%20%5Ccfrac%7B1676%7D%7B13%7D%3Dy%20%5Cblacktriangleleft%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cleft%28%20120~%2C~%5Cfrac%7B1676%7D%7B13%7D%20%5Cright%29~%5Chfill)