Solving a Linear System Using Substitution

SOLUTION:

\[ 5x + 3y = 10 \tag{1} \] \[ \;\;\;-x + y = -10 \tag{2} \] \[ \ \] \[ \;\;\;\;\;\;\;\;\Rightarrow\;\;\;\;\;\;y = -10 + x \tag{3} \] \[ \\ \] \[(3) \unicode{x2933} (1):\] \[ \ \] \[ \begin{aligned} 5x + 3(-10 + x) &= 10 \\ \\ 8x - 30 &= 10 \\ \\ \therefore x &= 5 \end{aligned} \] \[ \\ \] \[ \begin{aligned} (3)\longrightarrow y &= -10 + 5 \\ \\ &=-5 \end{aligned} \] \[ \\ \] \[ \therefore x = \underline{\underline{5}} \;\; ; \;\; y = \underline{\underline{-5}} \]