Question

How do you sovle 2x+2y=18 6x+y=39

Answer 1

6x+y=39;2x+2y=18

Solve 6x+y=39 for y:

6x+y+−6x=39+−6x(Add -6x to both sides)

y=−6x+39

Substitute (−6x+39) for y in 2x+2y=18:

2x+2y=18

2x+2(−6x+39)=18

−10x+78=18(Simplify both sides of the equation)

−10x+78+−78=18+−78(Add -78 to both sides)

−10x=−60

−10x/−10 = −60/−10(Divide both sides by -10)

x=6

Substitute (6) for x in y=−6x+39:

y=−6x+39

y=(−6)(6)+39

y=3

Answer: y = 3, x = 6

Answer 2

`\begin{cases} 2x+2y=18 \\ 6x+y=39 \end{cases} \\ \\ W=\left|\begin{array}{ccc}2&2\\6&1\end{array}\right| \ W_(x)=\left|\begin{array}{ccc}18&2\\39&1\end{array}\right| \ W_(y)=\left|\begin{array}{ccc}2&18\\6&39\end{array}\right| \\ \\ W=\left|\begin{array}{ccc}2&2\\6&1\end{array}\right|=2*1-6*2=2-12=-10 \\ \\ W_(x)=\left|\begin{array}{ccc}18&2\\39&1\end{array}\right|=18*1-2*39=-60 \\ \\ W_(y)=\left|\begin{array}{ccc}2&18\\6&39\end{array}\right|=2*39-6*18=-30`


`x= (W_(x))/(W) = (-60)/(-10)=6 \\ \\ y= (W_(y))/(W) = (-30)/(-10)=3`