4x+y=5 ;x+y=1 ?????

4x + y  = 5

  x + y = 1      | Subtraction      =>     3x = 4   =>      x = $${\frac{{\mathtt{4}}}{{\mathtt{3}}}}$$          y  = 1 - 4/3 = $${\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$

4x+y=5 (1)

x+y=1   (2)

(1)-(2)

3x=4

x=4/3

Sub into (2)

4/3 + y = 1

y=-1/3

4x+y=5 ;x+y=1 ?????      aking first-degree equations with two unknowns ?

$$\small{\text{$ \begin{array}{lccrcl} (1)&:& & 4x + y &=& 5 \\ (2)&:& & x + y &=& 1 \\ \hline &\\ (1) - (2)&:& & 4x - x + y - y &=& 5-1\\ & & & 3x &=& 4 \qquad |\qquad : 3\\ & & & \textcolor[rgb]{1,0,0}{x} &\textcolor[rgb]{1,0,0}{=}& \textcolor[rgb]{1,0,0}{ \frac{4}{3} }\\ \hline &\\ (2)&:& & x + y &=& 1 \\ & & & \frac{4}{3} +y &=& 1 \qquad |\qquad -\frac{4}{3}\\ & & & y &=& 1 -\frac{4}{3} \\ & & & \textcolor[rgb]{1,0,0}{y} &\textcolor[rgb]{1,0,0}{=}& \textcolor[rgb]{1,0,0}{-\frac{1}{3}} \\ \end{array} $}}$$