The given equations are
[tex] 5x+2y=10
\\
3x+2y=6 [/tex]
We can solve the system of equations by elimination , and for that, we will subtract the two equations, that is
[tex] 5x+2y-3x-2y=10-6
\\
2x = 4
\\
x =2 [/tex]
Back substituting the value of x,
[tex] 5(2)+2y =10
\\
10 + 2y=10
\\
2y=0
\\
y=0
[/tex]
So the required solution is (2,0).