Question

Solve the system using substitution. Show work.

{4x+5y=7
{y=3x+9

Answer 1

`\it \begin{cases}\it4x+5y=7 \\\;\\ \it y=3x+9 \ \ \ \ (*) \end{cases}`



`\it 4x+5y=7 \stackrel{(*)}{\Longrightarrow} 4x+5(3x+9) = 7 \Rightarrow 4x+15x+ 45 =7 \Rightarrow \\\;\\ \Rightarrow 4x+15x=7-45 \Rightarrow 19x= -38 \Rightarrow x = (-38)/(19) \Rightarrow x= -2`




`\it x=-2 \stackrel{(*)}{\Longrightarrow} y=3\cdot(-2) +9 \Rightarrow y=-6+9 \Rightarrow y=3 \\\;\\ So,\ we\ have: \begin{cases} \it x=-2 \\\;\\ \it y=3\end{cases}`