Question

Solve using elimination. 8x − 7y = –5 –x + 4y = –15

Answer 1

Steps
8x−7y=−5
Add 7y to both sides
8x−7y+7y=−5+7y
Simplify
8x=−5+7y
Divide both sides by 8
8x
8 =−
5
8 +
7y
8
Simplify
x=
−5+7y
8

Answer 2

Answer:

Therefore, the values of "x" and "y" are -1000/312 and -115/39 respectively.

Step-by-step explanation:

★ Solution :-

$\sf \leadsto 8x - 7y = -5 - - - (i)$

$\sf \leadsto -x + 4y = -15 - - - (ii)$

By first equation,

$\sf \leadsto 8x - 7y = -5$

$\sf \leadsto 8x = -5 + 7y$

$\sf \leadsto x = \dfrac{-5 + 7y}{8}$

Now, we can find the original value of y.

$\sf \leadsto -x + 4y = -15$

$\sf \leadsto \bigg( \dfrac{-5 + 7y}{8} \bigg) + 4y = -15$

$\sf \leadsto \dfrac{-5 + 7y}{8} + 4y = -15$

$\sf \leadsto \dfrac{-5 + 7y + 32y}{8} = -15$

$\sf \leadsto \dfrac{-5 + 39y}{8} = -15$

$\sf \leadsto -5 + 39y = -15(8)$

$\sf \leadsto -5 + 39y = -120$

$\sf \leadsto 39y = -120 + 5$

$\sf \leadsto 39y = - 115$

$\sf \leadsto y = \dfrac{ - 115}{39}$

Now, we can find the original value of x.

$\sf \leadsto 8x - 7y = -5$

$\sf \leadsto 8x -7 \bigg( \dfrac{ - 115}{39} \bigg) = -5$

$\sf \leadsto 8x + \dfrac{805}{39} = -5$

$\sf \leadsto \dfrac{312x + 805}{39} = -5$

$\sf \leadsto 312x + 805 = -5(39)$

$\sf \leadsto 312x + 805 = -195$

$\sf \leadsto 312x = -195 - 805$

$\sf \leadsto 312x = -1000$

$\sf \leadsto x = \dfrac{-1000}{312}$

$\textsf {\underline{Answer-}}$

Therefore, the values of x and y are -1000/312 and -115/39 respectively.