Let x be the gross production of products , and let y be the gross production of machinery and X= [ yx ]

• we have D =[588] and A = [0.20.60.20.2] so X should satisfy the equation X=AX + D then (I₂- A)X= D where (I₂- A) =[0.210.610.20.2] = [0.20.40.80.2]
• then [0.2x+0.8y0.4x0.2y] = [588] thus 0.4x - 0.2y = 88 and - 0.2x + 0.8y = 5
• then 2x - y = 440 (Eq1) and - x+ 4y = 25 (Eq2)
• 4(Eq1) + (Eq2) => 7x = 1785 thenx= 255andy= 2x-440 = 70

Hence:

• products255units
• machinery70units

I get confused on this step

• then 2x - y = 440 (Eq1) and - x+ 4y = 25 (Eq2)

how do we get those equations

also how do you come up with this part

• 4(Eq1) + (Eq2) => 7x = 1785 thenx= 255andy= 2x-440 = 70