Question

Solve using elimination.

8x − 7y = –5
–x + 4y = –15

Answer 1

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

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 = (-5 + 7y)/(8)`

Now, we can find the original value of y.

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

`\sf \leadsto \bigg( (-5 + 7y)/(8) \bigg) + 4y = -15`

`\sf \leadsto (-5 + 7y)/(8) + 4y = -15`

`\sf \leadsto (-5 + 7y + 32y)/(8) = -15`

`\sf \leadsto (-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 = ( - 115)/(39)`

Now, we can find the original value of x.

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

`\sf \leadsto 8x -7 \bigg( ( - 115)/(39) \bigg) = -5`

`\sf \leadsto 8x + (805)/(39) = -5`

`\sf \leadsto (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 = (-1000)/(312)`

`\textsf {\underline{Answer-}}\\`

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

Answer 2

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