Question

Solve for each System of Equation

(Any help on this topic is greatly appreciated)
`\left \{ {{5x-2y=4} \atop {2x-y=1}} \right.`

Answer 1

5x-2y=4 x=2 and y=3
2x-y=1 both x and y equals one

Answer 2

using substitution.

`\bf \begin{cases}5x-2y=4\\2x-y=1\end{cases}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\\stackrel{\textit{solving the 2nd equation for \underline{y}}}{2x-y=1\implies 2x-1=\boxed{y}}~\hspace{5em}\stackrel{\textit{substituting the found \underline{y} in the 1st equation}}{5x-2\left( \boxed{2x-1} \right)=4}\\\\\\5x-4x+2=4\implies x=4-2\implies \blacktriangleright x = 2\blacktriangleleft`

`\bf \stackrel{\textit{now, we substitute the found \underline{x} in the 1st equation}}{5(2)-2y=4\implies 10-2y=4}\implies 10-4=2y\\\\\\6=2y\implies \cfrac{6}{2}=y\implies \blacktriangleright 3=y \blacktriangleleft\\\\[-0.35em]\rule{34em}{0.25pt}\\\\~\hfill (2,3)~\hfill`