Question

Negative 4 x + 6 y = negative 18 and y = negative 2 x + 21

Answer 1

Correct Question

-4x + 6y = -18

y = -2x + 21

Answer

$\sf \dashrightarrow -4x + 6y = -18 \: \: (i)$

$\sf \dashrightarrow y = -2x + 21 \: \: (ii)$

By first equation,

$\sf \dashrightarrow -4x + 6y = -18$

$\sf \dashrightarrow -4x = -18 - 6y$

$\sf \dashrightarrow x = \dfrac{-18 - 6y}{4}$

Now, let's find the value of y by second equation.

$\sf \dashrightarrow y = -2x + 21$

$\sf \dashrightarrow -2x - y = -21$

$\sf \dashrightarrow -2 \bigg( \dfrac{-18 - 6y}{4} \bigg) - y = -21$

$\sf \dashrightarrow \dfrac{36 + 12y}{4} - y = -21$

$\sf \dashrightarrow \dfrac{36 + 12y - 4y}{4} = -21$

$\sf \dashrightarrow \dfrac{36 + 8y}{4} = -21$

$\sf \dashrightarrow 36 + 8y = -21 \times 4$

$\sf \dashrightarrow 36 + 8y = -84$

$\sf \dashrightarrow 8y = -84 - 36$

$\sf \dashrightarrow 8y = -120$

$\sf \dashrightarrow y = \dfrac{-120}{8}$

$\sf \dashrightarrow y = -15$

Now, let's find the value of x by first equation.

$\sf \dashrightarrow -4x + 6y = -18$

$\sf \dashrightarrow 4x + 6(-15) = -18$

$\sf \dashrightarrow 4x + (-90) = -18$

$\sf \dashrightarrow 4x - 90 = -18$

$\sf \dashrightarrow 4x = -18 + 90$

$\sf \dashrightarrow 4x = 72$

$\sf \dashrightarrow x = \dfrac{72}{4}$

$\sf \dashrightarrow x = 18$

Hence, the values of x and y are 18 and -15 respectively.