Question

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

Answer 1

Answer:

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

Step-by-step 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:

$\displaystyle \: \frac{16y}{16} = \frac{ - 48}{16} \\ y = - 3$

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

$\displaystyle \: \frac{4x}{4} = \frac{ - 4}{4} \\ x = - 1$

therefore our solution is

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

Answer 2

Answer:

Solution given:

-3x+7y=-18

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

4x-4y=8

4(x-y)=8

x-y=$\frac{8}{2}$

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=$\frac{12}{ - 4}$=-3

substituting value of y in equation 2,we get

x-(-3)=2

x=2-3

x=-1

:.

x=-1

y=-3