Question

Solve the system of equations -3x+7y=-18 and 4x-4y=8 by combining the equations.

Explaining Is Required​

Answer 1

`\huge \colorbox{red}{(x,y)=(-1,-3)}`

Explanation:

multiply first equation by 4 and second by 3 respectively:

`\begin{cases} \displaystyle - 12x + 28y = - 72 \\ \: \: \displaystyle \: 12x - 12y = 24 \end{cases}`

combine the equations:

`\underline{ \begin{cases} \displaystyle - 12x + 28y = - 72 \\ \: \: \displaystyle \: 12x - 12y = 24 \end{cases}} \\ \displaystyle16y = - 48`

divide both sides by -48:

`\displaystyle \: (16y)/(16) = ( - 48)/(16) \\ y = - 3`

substitute the value of y to the second equation

`\displaystyle \: 4x - 4. - 3 = 8`

simplify multiplication:

`\displaystyle \: 4x + 12 = 8`

cancel 12 from both sides:

`\displaystyle \: 4x = - 4`

divide both sides by 4

`\displaystyle \: (4x)/(4) = ( - 4)/(4) \\ x = - 1`

therefore our solution is

`\displaystyle (x,y)=(-1,-3)`

Answer 2

Solution given:

-3x+7y=-18

3x-7y=18.................[1]

4x-4y=8

4(x-y)=8

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

x-y=2..........….........[2]

multiplying equation 2 by 3 and subracting equation 1 and 2,we get

`3x-7y - 3x + 3y = 18 - 6`

-4y=12

y=
`(12)/( - 4)`=-3

substituting value of y in equation 2,we get

x-(-3)=2

x=2-3

x=-1

:.

x=-1

y=-3