Answer:
![h\neq 7.5](https://tex.z-dn.net/?f=h%5Cneq%207.5)
k = -4
Step-by-step explanation:
Given system of equations are,
-3x-3y = h
-4x + ky = 10
We have to find the values of h and k such that system of equations has no solution.
The standard form of system of equation in two variables can be given by,
![a_1x+b_1y+c_1=0](https://tex.z-dn.net/?f=a_1x%2Bb_1y%2Bc_1%3D0)
![a_2x+b_2y+c_2=0](https://tex.z-dn.net/?f=a_2x%2Bb_2y%2Bc_2%3D0)
And condition for the system of equations has no solution is given by,
![\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba_1%7D%7Ba_2%7D%3D%5Cdfrac%7Bb_1%7D%7Bb_2%7D%5Cneq%20%5Cdfrac%7Bc_1%7D%7Bc_2%7D)
So, by comparing the standard form of equations with given equations, the condition such that system has no solution can be written as,
![\dfrac{-3}{-4}=\dfrac{-3}{k}\neq \dfrac{h}{10}](https://tex.z-dn.net/?f=%5Cdfrac%7B-3%7D%7B-4%7D%3D%5Cdfrac%7B-3%7D%7Bk%7D%5Cneq%20%5Cdfrac%7Bh%7D%7B10%7D)
![=>\dfrac{-3}{-4}=\dfrac{-3}{k}](https://tex.z-dn.net/?f=%3D%3E%5Cdfrac%7B-3%7D%7B-4%7D%3D%5Cdfrac%7B-3%7D%7Bk%7D)
=> k = -4
and ![\dfrac{-3}{-4}\neq \dfrac{h}{10}](https://tex.z-dn.net/?f=%5Cdfrac%7B-3%7D%7B-4%7D%5Cneq%20%5Cdfrac%7Bh%7D%7B10%7D)
![=>\ \dfrac{-3\times 10}{-4}\neq h](https://tex.z-dn.net/?f=%3D%3E%5C%20%5Cdfrac%7B-3%5Ctimes%2010%7D%7B-4%7D%5Cneq%20h)
![=>\ h\neq \dfrac{30}{4}](https://tex.z-dn.net/?f=%3D%3E%5C%20h%5Cneq%20%5Cdfrac%7B30%7D%7B4%7D)
![=>\ h\neq 7.5](https://tex.z-dn.net/?f=%3D%3E%5C%20h%5Cneq%207.5)
So, the value of h and k for above given system of equations is
and k = -4.