The cost of three notebooks and four pencils is $7.20. The cost of five notebooks and eight pencils is $13.20. Write a system of equations to model this situation. How much does one pencil and one notebook cost?

Answer:Notebook cost = $1.2Pencil cost = $ 0.9Step-by-step explanation:Call x at the cost of each notebook and call z at the cost of each pencil.So we know that 3x added with 4z equals $ 7.20So:[tex]3x + 4z = \$ 7.20[/tex]    (i)We also know that 5x and 8z = $13.20Then:[tex]5x + 8z = \$13.20[/tex]    (ii)Finally we have a system of 2 equations (i), (ii) and two unknowns x and z.Then we can solve the system by doing:-2(i) + (ii)We have left:[tex]-6x - 8z = \$-14.4[/tex]        +[tex]5x + 8z = \$13.20[/tex]---------------------------------------[tex]-x = -1.2\\x = \$1.2[/tex]Now we substitute the value of x in equation (i) and clear z.[tex]3(1.2) + 4z = \$7.20\\\\4z = 3.6\\\\z = \$0.9[/tex]