Question

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

Answer 1

Explanation:

-3x+7y = -18 ...1

4x-4y = 8 ...2

...1 × 4

-12x + 28y = -72 ...3

...2 × 3

12x - 12y = 24 ...4

...3 + ...4

28y - 12y = -72 + 24

16y = -48

y = -3

Replace y = -3 in ...2

4x - 4(-3) = 8

4x + 12 = 8

4x = 8 - 12

4x = -4

x = -1

Answer 2

`\huge\boxed{\boxed{(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)`