Question

Identify the best method for solving the given

system of equations. DO NOT SOLVE. Justify your
choice using academic vocabulary.


y=x+4
3x – 4y = -19

Answer 1

The solution is:

`y=7,\:x=3`

Explanation:

I think substitution method would be the best method for solving the given system of equations.

The reason is that all we need is to plug in the the value of y i.e. y=x+4 in the equation 3x – 4y = -19, then solve for x, and in the end substitute the value x in the equation y=x+4 to get the y-value.

The other method, elimination method, can also be used, but elimination method in current system of the equations would involve a certain degree of arrangements of the variables and then different multiplying of the equation to eliminate the variables.

Thus, I think substitution method would be the best method for solving the given system of equations.

Let us solve using substitution method

`\begin{bmatrix}y=x+4\\ 3x-4y=-19\end{bmatrix}`

`\mathrm{Subsititute\:}y=x+4`

`\begin{bmatrix}3x-4\left(x+4\right)=-19\end{bmatrix}`

`\begin{bmatrix}-x-16=-19\end{bmatrix}`

`x=-16+19`

`x=3`

Now, just substitute x=3 in y=x+4

`y=x+4`

`y=3+4`

`y=7`

Thus, the solution is:

`y=7,\:x=3`