Question

1 1 What is the value of k, if (k, 5) is the solution of the simultan equations 4x + 3y = 19 and 4x - 3y = -11?​

Answer 1

Step-by-step explanation:

Question :-

What is the value of k, if (k, 5) is the solution of the simultaneous equations 4x + 3y = 19 and 4x - 3y = -11 ?

Solution :-

Since, (k, 5) is the solution of simultaneous equation,

Therefore, it should satisfy the given equations

${\bold{⟼ \: \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{4(k) \: + \: 3(5) \: = \: 19}}}}$

${\bold{⟼ \: \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{4k \: + \: 15 \: = \: 19}}}}$

${\bold{⟼ \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{4k \: = \: 19 \: - \: 15}}}}$

${\bold{⟼ \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{4k \: = \: 4}}}}$

${\bold{⟼ \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{k \: = \: \frac{4}{4}}}}}$

${\bold{⟼ \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{k \: = \: 1}}}}$

Also,

${\bold{⟼ \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{4k \: - \: 3(5) \: = \: -11}}}}$

${\bold{⟼ \: \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{4k \: - \: (15) \: = \: -11}}}}$

${\bold{⟼ \: \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{4k \: = \: -11 \: + \: 15}}}}$

${\bold{⟼ \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{4k \: = \: 4}}}}$

${\bold{⟼ \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{k \: = \: \frac{4}{4}}}}}$

${\bold{⟼ \: \: \: \: \: \: \: \: \: \: }}{\large{\rm{\blue{k \: = \: 1}}}}$

Therefore the value of k is 1