Question

Solve by substitution:
y=x-12
8x+8y=-16

Answer 1

G I V E N :

Solve by substitution :

y = x - 12

8x + 8y = -16

S O L U T I O N :

y = x - 12 ------- eq(1)

8x + 8y = -16 ------- eq(2)

Finding x ⤵

Putting y = x - 12 in eq(2) we get

• 8x + 8(x - 12) = -16

• 8x + 8x - 96 = -16

• 16x = 96 - 16

• 16x = 80

• x = 80/16

• x = 5

Finding y ⤵

Putting x = 5 in eq(1) we get

• y = x - 12

• y = 5 - 12

• y = -7

Hence, x is 5 and y is -7

Answer 2

`(x,y) = ( 5 , - 7)`

Explanation:

we would like to solve the following system of linear equation by substitution:

`\displaystyle \begin{cases} y = x - 12\\ 8x + 8y = - 16\end{cases}`

notice that, we're already given the value of y therefore simply substitute it to the II equation

`8x + 8(x - 12) = - 16`

distribute:

`8x + 8x - 96= - 16`

simplify addition:

`16 x- 96= - 16`

isolate -96 to left hand side and change its sign:

`16 x= - 16 + 96`

simplify addition:

`16 x= 80`

divide both sides by 16 and that yields:

`\boxed{x= 5}`

now substitute the got value of x to the first equation:

`y = 5- 12`

simplify subtraction:

`y = - 7`

hence,

the solution is (x,y)=(5,-7)