Let the number of silk be
[tex]=x[/tex]Let the number of cottons be
[tex]=y[/tex]The total number of silk and cotton is 4.25 yards and this can be represented as
[tex]=x+y=4.25\ldots\ldots\text{.}\mathrm{}(1)[/tex]Silk is $16.90 per yard and cotton is $4 per yard has a total of $36.35
[tex]16.90x+4y=$36.35$\ldots\ldots\ldots(2)[/tex]From equation one, we can get an equation 3 which will be used to solve simultaneously
[tex]\begin{gathered} x+y=4.25 \\ y=4.25-x\ldots\ldots(3) \end{gathered}[/tex]Using substitution method, substitute equation (3) in equation (2)
[tex]\begin{gathered} 16.90x+4y=$36.35$ \\ 16.90x+4(4.25-x)=$36.35$ \\ 16.90x+17-4x=36.35 \\ \end{gathered}[/tex]Collect similar terms
[tex]\begin{gathered} 16.90x+17-4x=36.35 \\ 16.90x-4x=36.35-17 \\ 12.90x=19.35 \\ \text{divide both sides by 12.90} \\ \frac{12.90x}{12.90}=\frac{19.35}{12.90} \\ x=1.5 \end{gathered}[/tex]Substitute x= 1.5 in eqaution (3)
[tex]\begin{gathered} y=4.25-x \\ y=4.25-1.5 \\ y=2.75 \end{gathered}[/tex]Alternatively,
Using the graphical method, we will have
Therefore,
The value of x = 1.5 , the value of y = 2.75
