Ta có \(\dfrac{7-x}{13+y}=\dfrac{7}{13}\Rightarrow\dfrac{7-x}{7}=\dfrac{13+y}{13}\)

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\dfrac{7-x}{7}=\dfrac{13+y}{13}=\dfrac{13+y-7+x}{13-7}=\dfrac{6+x+y}{6}=\dfrac{2022+6}{6}=338\)

\(\Rightarrow\left\{{}\begin{matrix}7-x=338\times7=2366\\13+y=338\times13=4394\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-2359\\y=4381\end{matrix}\right.\)

Ta có \(\dfrac{7-x}{13+y}=\dfrac{7}{13}\Rightarrow\dfrac{7-x}{7}=\dfrac{13+y}{13}\)

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\dfrac{7-x}{7}=\dfrac{13+y}{13}=\dfrac{13+y-7+x}{13-7}=\dfrac{6+x+y}{6}=\dfrac{2022+6}{6}=338\)

\(\Rightarrow\left\{{}\begin{matrix}7-x=338\times7=2366\\13+y=338\times13=4394\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-2359\\y=4381\end{matrix}\right.\)

Tính đúng  y = 4 2 3

y = 4 2 3

(3x - 4)¹⁰ - 3 = 1021

(3x - 4)¹⁰ = 1024 = 2¹⁰

=>3x - 4 = 2

3x = 6

x = 2

\(\left(3x-4\right)^{10}-3=1021\)

\(\Rightarrow\orbr{\begin{cases}3x-4=\sqrt[10]{1024}\\3x-4=-\sqrt[10]{1024}\end{cases}}\Rightarrow\orbr{\begin{cases}3x-4=2\\3x-4=-2\end{cases}}\Rightarrow\orbr{\begin{cases}3x=6\\3x=2\end{cases}}\Rightarrow\orbr{\begin{cases}x=2\\x=\frac{2}{3}\end{cases}}\) 

Vậy: \(\orbr{\begin{cases}x=2\\x=\frac{2}{3}\end{cases}}\)

13y+5y-12y=1200

6y=1200

=>  y x (13+5-12) =1200

=>y x 6 =1200

=>y = 1200: 6

=> y= 200

=>  y(13+5-12) =1200

=>y6 =1200

=>y = 1200: 6

=> y= 200