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=(17)/(-7) \\ \text{then} \\ x=-(17)/(7) \end{gathered}`

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

`y=3(-(17)/(7))+5`

which gives

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

or equivalently,

`\begin{gathered} y=-(51)/(7)+(35)/(7) \\ y=(-51+35)/(7) \\ y=-(16)/(7) \end{gathered}`

Therefore, the solution of the given system is:

`\begin{gathered} x=-(17)/(7) \\ y=-(16)/(7) \end{gathered}`

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

`(-(17)/(7),-(16)/(7))`