Let x be price of one notebook and y be price of one package of pen.
The equation for cost of 5 notebooks and two package of pens are,
[tex]5x+2y=42.15[/tex]The equation for cost of three notebook and four package of pens is,
[tex]3x+4y=36.35[/tex]So system of equations for the cost of one notebook and one package of pen is,
5x + 2y = 42.15
3x + 4y = 36.35
PART B
Multiply the equation 5x + 2y = 42.15 by 2 to obtain the same coefficient of y.
[tex]\begin{gathered} 2(5x+2y=42.15) \\ 10x+4y=84.3 \end{gathered}[/tex]Substract equation 3x +4y = 36.35 from equation 10x + 4y = 84.3 to obtain the value of x.
[tex]\begin{gathered} 10x+4y-(3x-4y)=84.3-36.35 \\ 7x=47.95 \\ x=\frac{47.95}{7} \\ =6.85 \end{gathered}[/tex]Substitute 6.85 for x in equation 3x +4y = 36.35 to obtain the value of y.
[tex]\begin{gathered} 3\cdot6.85+4y=36.35 \\ 4y=36.35-20.55 \\ y=\frac{15.8}{4} \\ =3.95 \end{gathered}[/tex]The price of a notebook is $6.85 and price of a package of pen is $3.95.
