Question

decide whether it would be more convenient to solve the system of equations by substitution or elimination. x = 5y/3 "-9" 6x - y/4 = "-14"

Answer 1

By Substitution

STEP BY STEP EXPLANATION

`\begin{gathered} x\text{ = }(5y)/(3)\text{ - 9} \\ 6x\text{ - }(y)/(4)\text{ = -14} \end{gathered}`

Now, let's apply the substitution method

`\begin{gathered} 6((5y)/(3)\text{ - 9) - }(y)/(4)\text{ = -14} \\ 6(\frac{5y\text{ - 27}}{3})\text{ - }(y)/(4)\text{ = -14} \end{gathered}`
`\begin{gathered} 2(5y\text{ - 27) - }(y)/(4)\text{ = -14} \\ \frac{8(5y\text{ - 27) - y}}{4}\text{ = -14} \\ 40y\text{ - }216\text{ - y = }-56 \\ 39y\text{ = -56 + 216} \\ y\text{ = }(160)/(39) \end{gathered}`

Let's try Elimination method now to see the difference

`\begin{gathered} x\text{ = }(5y)/(3)\text{ - 9} \\ 3x\text{ = 5y - 27} \\ 5y\text{ - 3x = 27}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(1) \end{gathered}`