Question

Solve the following system:$\begin{gathered}y = 3x + 5 \\ 5x - 4y = - 3\end{gathered}$can you explain how to do this

Answer 1

We have the following system of equations:

$\begin{gathered} y=3x+5\ldots(A) \\ 5x-4y=-3\ldots(B) \end{gathered}$

Solving by substituting method.

By substituting equation (A) into (B), we have

$5x-4(3x+5)=-3$

now, by distributing the number 4 into the panrentheses, we get

$5x-12x-20=-3$

By combining similar terms, we obtain

$-7x-20=-3$

Now, by adding 20 to both sides, we have

$-7x=17$

and by dividing both sides by -7, we get

$\begin{gathered} x=\frac{17}{-7} \\ \text{then} \\ x=-\frac{17}{7} \end{gathered}$

Once we know the result for x, we can subtitute that value into equation (A) and get

$y=3(-\frac{17}{7})+5$

which gives

$\begin{gathered} y=3(-\frac{17}{7})+5 \\ y=-\frac{51}{7}+5 \end{gathered}$

or equivalently,

$\begin{gathered} y=-\frac{51}{7}+\frac{35}{7} \\ y=\frac{-51+35}{7} \\ y=-\frac{16}{7} \end{gathered}$

Therefore, the solution of the given system is:

$\begin{gathered} x=-\frac{17}{7} \\ y=-\frac{16}{7} \end{gathered}$

In order pair notation (x,y), the answer is expressed as:

$(-\frac{17}{7},-\frac{16}{7})$