Question

What is the solution for this: 7y + 3x =9if y= 9/7 -3x/7 and x= 3 -7y/3

Answer 1

Substituting x= 3 -7y/3​ into y= 9/7 -3x/7, we have

`y=(9)/(7)-(3(3-(7y)/(3)))/(7)`

Therefore,

`7y=9-3(3-(7y)/(3))=9-9+7y`

This implies that,

`\begin{gathered} 7y=7y \\ \Rightarrow0=0 \end{gathered}`

So the number of solutions is infinite.

We can set x = 1, then

`y=(9)/(7)-(3)/(7)=(6)/(7)`

Hence, (1, 6/7) is a solution

We can also set y = 3, then

`x=3-(7\mleft(3\mright))/(3)=3-7=-4`

Hence, (3, -4) is another solution