Чтобы найти точку пересечения, нужно решить систему:
![image](https://tex.z-dn.net/?f=%3C%2Fp%3E%3Cp%3E%5Cbegin%7Bcases%7D%3C%2Fp%3E%3Cp%3E2x-y%3D0%20%5C%5C%3C%2Fp%3E%3Cp%3Ex%2By%3D6%3C%2Fp%3E%3Cp%3E%5Cend%7Bcases%7D%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Cbegin%7Bcases%7D%20%3C%2Fp%3E%3Cp%3E2x-y%3D0%20%5C%5C%3C%2Fp%3E%3Cp%3Ey%3D6-x%3C%2Fp%3E%3Cp%3E%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E2x-%286-x%29%3D0%20%5C%5C%3C%2Fp%3E%3Cp%3E2x-6%2Bx%3D0%20%5C%5C%3C%2Fp%3E%3Cp%3E3x%3D6%20%5C%5C%3C%2Fp%3E%3Cp%3Ex%3D2%20%5C%5C%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3Ey%3D6-2%20%5C%5C%3C%2Fp%3E%3Cp%3Ey%3D4%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Cbegin%7Bcases%7D%3C%2Fp%3E%3Cp%3E2%5Ccdot%202%20-%204%20%3D0%20%5C%5C%3C%2Fp%3E%3Cp%3E2%20%2B%204%20%3D6%3C%2Fp%3E%3Cp%3E%5Cend%7Bcases%7D%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%5Cbegin%7Bcases%7D%3C%2Fp%3E%3Cp%3E0%3D0%20%5C%5C%3C%2Fp%3E%3Cp%3E6%3D6%3C%2Fp%3E%3Cp%3E%5Cend%7Bcases%7D%20)
\begin{cases}
2x-y=0 \\
x+y=6
\end{cases} \\\\
\begin{cases}
2x-y=0 \\
y=6-x
\end{cases} \\\\\\
2x-(6-x)=0 \\
2x-6+x=0 \\
3x=6 \\
x=2 \\\\\\
y=6-2 \\
y=4 \\\\
\begin{cases}
2\cdot 2 - 4 =0 \\
2 + 4 =6
\end{cases} \\\\
\begin{cases}
0=0 \\
6=6
\end{cases} " alt="
\begin{cases}
2x-y=0 \\
x+y=6
\end{cases} \\\\
\begin{cases}
2x-y=0 \\
y=6-x
\end{cases} \\\\\\
2x-(6-x)=0 \\
2x-6+x=0 \\
3x=6 \\
x=2 \\\\\\
y=6-2 \\
y=4 \\\\
\begin{cases}
2\cdot 2 - 4 =0 \\
2 + 4 =6
\end{cases} \\\\
\begin{cases}
0=0 \\
6=6
\end{cases} " align="absmiddle" class="latex-formula">
Пара является решением, значит x = 2, а y = 4.
Точка пересечения: ( 2 , 4 ).