Question

solve this equation
p+q =43
44p+54q=2137​

Answer 1

p + q = 43

44p + 54q = 2137

________ [GIVEN EQUATIONS]

• p + q = 43

=> p = 43 - q ________ (eq 1)

• 44p + 54q = 2137

=> 44(43 - q) + 54q = 2137

=> 1892 - 44q + 54q = 2137

=> 10q = 2137 - 1892

=> 10q = 245

=> q = $\dfrac{245}{10}$

=> q = $\dfrac{49}{5}$

Put value of q in (eq 1)

=> p = 43 - $\dfrac{49}{5}$

=> p = $\dfrac{215\:-\:49}{5}$

=> p = $\dfrac{166}{5}$

______________________________

$\bold{p\:=\:\dfrac{166}{5}}$

$\bold{q\:=\:\dfrac{49}{5}}$

___________ $\bold{[ANSWER]}$

______________________________

Now..

We have p = $\dfrac{166}{5}$ and q = $\dfrac{49}{5}$

Put value of p and q in (eq 1) i.e.

p + q = 43

=> $\dfrac{166}{5}$ + $\dfrac{49}{5}$ = 43

=> $\dfrac{215}{5}$ = 43

=> 43 = 43

_______ [HENCE VERIFIED]

______________________________

Answer 2

p + q = 43

p = 43 - q

Also,

44p + 54q = 2137

44(43 - q) + 54q = 2137

1892 - 44q + 54q = 2137

10q = 2137 - 1892

10q = 245

• q = 245/10 = 49/5

Now,

p = 43 - 49/5

• p = 166/5