Question

Solve the system by substitution.y =10xY=4x+22

Answer 1

Given the system:

`\begin{cases}y=10x \\ y=4x+22\end{cases}`

Let's clear x from equation 1:

`\begin{gathered} y=10x\rightarrow(y)/(10)=x \\ \rightarrow x=(y)/(10)\text{ (A)} \end{gathered}`

And substitute (A) in equation 2:

`\begin{gathered} y=4x+22 \\ \rightarrow y=4((y)/(10))+22 \\ \rightarrow y=(4)/(10)y+22 \end{gathered}`

Solving for y:

`\begin{gathered} y=(4)/(10)y+22 \\ \rightarrow y-(4)/(10)y=22 \\ \rightarrow(3)/(5)y=22\rightarrow3y=110\rightarrow y=(110)/(3) \end{gathered}`

Now, let's use (A) to calculate x:

`\begin{gathered} x=(y)/(10) \\ \rightarrow x=((110)/(3))/((10)/(1))\rightarrow x=(110)/(30)\rightarrow x=(11)/(3) \end{gathered}`

This way,

`\begin{gathered} x=(11)/(3) \\ \\ y=(110)/(3) \end{gathered}`