Question

Determine all values of h and k for which the system S 1 -3x - 3y = h -4x + ky = 10 has no solution. k= ht

Answer 1

`h\\eq 7.5`

k = -4

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`

`a_2x+b_2y+c_2=0`

And condition for the system of equations has no solution is given by,

`(a_1)/(a_2)=(b_1)/(b_2)\\eq (c_1)/(c_2)`

So, by comparing the standard form of equations with given equations, the condition such that system has no solution can be written as,

`(-3)/(-4)=(-3)/(k)\\eq (h)/(10)`

`=>(-3)/(-4)=(-3)/(k)`

=> k = -4

and
`(-3)/(-4)\\eq (h)/(10)`

`=>\ (-3* 10)/(-4)\\eq h`

`=>\ h\\eq (30)/(4)`

`=>\ h\\eq 7.5`

So, the value of h and k for above given system of equations is

`h\\eq 7.5` and k = -4.