Question

Solve the system 4x-2y=5 and 4x+y=-4

Answer 1

`\bf \begin{cases} 4x-2y=5\\[1em] 4x+y=-4\implies \boxed{y}=-4-4x \end{cases} \\\\\\ \stackrel{\textit{plugging in \boxed{y} in the 1st equation}}{4x-2\left( \boxed{-4-4x} \right)=5}\implies 4x+8+8x=5 \\\\\\ 12x=-3\implies x=\cfrac{-3}{12}\implies \blacktriangleright x=-\cfrac{1}{4} \blacktriangleleft`

`\bf \boxed{y}=-4-4x\implies y=-4-4\left( -\cfrac{1}{4} \right)\implies y=-4+1\implies \blacktriangleright y=-3 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( -(1)/(4)~~,~~-3 \right)~\hfill`

Answer 2

-1 ( 4x -2y = 5) 4x +(-3) = -4
4x -3 = -4
-4x + 2y = -5 +3 +3
4x + y = -4 _______
___________
0x + 3y = -9 4x= -1
______ ______
3 4
y= -3 x= -1/4