Question

Solve for x and y.
11x + 15y + 23 = 0, 7x - 2y - 20 = 0​

Answer 1

Answer

The given equations are,

$\sf \dashrightarrow 11x + 15y = - 23 \: - - - (i)$

$\sf \dashrightarrow 7x - 2y = 20 \: - - - (ii)$

Multiplying (i) by 2 and (ii) by 15 and adding the results, we get

$\sf \dashrightarrow 22x + 105x = - 46 + 300$

Adding the values on LHS and RHS,

$\sf \dashrightarrow 127x = 254$

$\sf \dashrightarrow x = \dfrac{254}{127} = 2$

Putting x = 2 in (i), we get

$\sf \dashrightarrow 22 + 15y = - 23$

$\sf \dashrightarrow 15y = - 23 - 22$

Subtracting the values on RHS,

$\sf \dashrightarrow 15y = - 45$

$\sf \dashrightarrow y = \dfrac{-45}{15}$

Simplifying the fraction,

$\sf \dashrightarrow - 3$

Hence,

$\sf \dashrightarrow \boxed{\sf x = 2 \: \: \: and \: \: \: y = - 3}$