Find cost of each item

Question

alison went back to school shopping with her three children. her first child needed three notebooks, four pencils and two pens for a total of $5.45. her second child need five notebooks,two pencils and three pens totaling $7.80. her last child needs two notebooks, four pencils and four pens for a total cost of $5.25

Answer 1

X = notebook

Y = pencil

Z = pen

3X + 4 Y + 2Z = 545

5X + 2Y + 3Z = 780

2X + 4Y + 4Z = 525

-2*eq2 + e1 : -7x -4z = -1015

7x + 4z = 1015 <--- alpha

-2*e2 + e3:

-8x - 2z = -1035

8x + 2z = 1035 <-- beta

-2 * beta + alpha:

-9x = - 1055

x = -1055/-9 = 117.2

z= 48.61

3x + 4y + 2z = 545

3(117.2) + 4y + 2(48.61) = 545

y=24.03