Solution:
Let number of buttons in Shirt = x
And Number of buttons in Jackets = y
36 shirts and 42 jackets contains 842 buttons.
And collection of 6 shirts and 7 jackets contains 137 buttons.
Writing it in terms of equations
→ 36 x + 42 y = 842 -------(1)
→ 6 x + 7 y = 137-----(2) × 6
→ 36 x +42 y = 822 ----(3)
As equation (1) and (3) are such that there x and y coefficient are same , but the constant term on one side of equation are different. It means the two equation have no solution.
I.e → ![\frac{a_{1}}{a_{2}} =\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Ba_%7B1%7D%7D%7Ba_%7B2%7D%7D%20%3D%5Cfrac%7Bb_%7B1%7D%7D%7Bb_%7B2%7D%7D%20%20%5Cneq%20%5Cfrac%7Bc_%7B1%7D%7D%7Bc_%7B2%7D%7D)
So, the two equation have no solution.
It means we can't find number of buttons in jackets and shirts.