Question

Solve the system {2x+y=8 using substitution method.

{x-y=6 using elimination method


please answer my question ​

Answer 1

`\large\huge\green{\sf{Answer:-}}`

`\red {\mathbb{ \underline { \tt by \: elimination \: method \: s}}}`

• 2x+y=8________(i)
• x-y=6_________(ii)

from equation (i):-

`2x - y = 8 \\ x = (8 - y)/(2)`

• put value of x in eq (ii)

`x - y = 6 \\ (8 - y)/(2) - y = 6 \\ (8 - y - 2y)/(2) = 6 \\ 8 - y - 2y = 12 \\ 8 - 3y = 12 \\ - 3y = 12 - 8 \\ - 3y = 4 \\ y = ( - 4)/(3)`

• put value of y in eq (i)

`2x + y = 8 \\ 2x + ( ( - 4)/(3) ) = 8 \\ 2x - \frac { 4}{3} = 8 \\ (6x - 4)/(3) = 8 \\ 6x - 4 = 8 * 3 \\ 6x - 4 = 24 \\ 6x = 24 + 4 \\ 6x = 28 \\ x = (14)/(3)`

now,

By elimination method:-

`2x + y = 8 \\ x - y = 6 \\ - - - - - - - \\ multiply \: eq \: (i) \: by \: 1 \\ and \: eq(ii) \: by \: 2 \\ \\ (2x + y = 8) * 1\\ (x - y = 6) * 2 \\ - - - - - - - \\2x + y = 8 \\ 2x - 2y = 12 \\ subtract \: these \\ 3y = - 4 \\ y = ( - 4)/(3) \\`

put value of y in equation (i)

`2x + y = 8 \\ 2x + ( ( - 4)/(3) ) = 8 \\ 2x - \frac { 4}{3} = 8 \\ (6x - 4)/(3) = 8 \\ 6x - 4 = 8 * 3 \\ 6x - 4 = 24 \\ 6x = 24 + 4 \\ 6x = 28 \\ x = (14)/(3)`

Answer 2

y = -4/3

x = 14/3

Explanation:

2x+y=8

x-y=6

First of all, we need the same coefficient, so we can make both of these 2x by multiplying the second one by 2.

2x+y=8

2x-2y=12

Then we need to subtract equation 1 from 2.

3y=-4

Solve normally

y = -1.33333 / -4/3

Substitute

x - (-4/3) = 6

x = 14/3