Question

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

Answer 1

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

$x= \frac{W_{x}}{W} = \frac{-60}{-10}=6 \\ \\ y= \frac{W_{y}}{W} = \frac{-30}{-10}=3$

Answer 2

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