Respuesta :
Given the system:
[tex]\begin{cases}y=10x \\ y=4x+22\end{cases}[/tex]Let's clear x from equation 1:
[tex]\begin{gathered} y=10x\rightarrow\frac{y}{10}=x \\ \rightarrow x=\frac{y}{10}\text{ (A)} \end{gathered}[/tex]And substitute (A) in equation 2:
[tex]\begin{gathered} y=4x+22 \\ \rightarrow y=4(\frac{y}{10})+22 \\ \rightarrow y=\frac{4}{10}y+22 \end{gathered}[/tex]Solving for y:
[tex]\begin{gathered} y=\frac{4}{10}y+22 \\ \rightarrow y-\frac{4}{10}y=22 \\ \rightarrow\frac{3}{5}y=22\rightarrow3y=110\rightarrow y=\frac{110}{3} \end{gathered}[/tex]Now, let's use (A) to calculate x:
[tex]\begin{gathered} x=\frac{y}{10} \\ \rightarrow x=\frac{\frac{110}{3}}{\frac{10}{1}}\rightarrow x=\frac{110}{30}\rightarrow x=\frac{11}{3} \end{gathered}[/tex]This way,
[tex]\begin{gathered} x=\frac{11}{3} \\ \\ y=\frac{110}{3} \end{gathered}[/tex]