use the system of substituion

x+2y=7     rearrange this as  x = 7 - 2y   (1)

2x+2y=13    (2)

Substitute (1)  into (2)  for x   and we have

2[ 7 - 2y] + 2y = 13

14 - 4y + 2y  = 13

14 - 2y  = 13       subtract 14 from both sides

-2y  = -1              divide both sides by -2

y = 1/2

And using (1) ....  x = 7 - 2(1/2)  =  7 - 1   = 6

So     ...      {x, y}   = { 6, 1/2 }

x+2y=7

2x+2y=13

\(\begin{array}{lrcll} (1)& x+2y &=& 7 \quad & | \quad -x\\ & 2y &=& 7 -x \\\\ (2)& 2x+2y &=& 13 \\ & 2x +(7-x) &=& 13 \\ & 2x + 7-x &=& 13 \\ & x + 7 &=& 13 \quad & | \quad -7\\ & x &=& 13 -7\\ & \mathbf{x} & \mathbf{=} & \mathbf{6} \\\\ & 2y &=& 7 -x \\ & 2y &=& 7 -6 \\ & 2y &=& 1 \quad & | \quad :2\\ & y &=& \frac12\\ & \mathbf{y} & \mathbf{=} & \mathbf{0.5} \\\\ \end{array}\)