Use the diagram to work out the solution to these simultaneous equations: \[ \begin{array}{l} y=-2 x+7 \\ y=\frac{1}{2} x+1 \end{array} \]

Step 1 ：Since both equations are already in the form of y, we can set them equal to each other: \(-2x + 7 = \frac{1}{2}x + 1\)

Step 2 ：Add 2x to both sides: \(7 = \frac{5}{2}x + 1\)

Step 3 ：Subtract 1 from both sides: \(6 = \frac{5}{2}x\)

Step 4 ：Divide both sides by \(\frac{5}{2}\): \(x = \frac{12}{5}\)

Step 5 ：Substitute the value of x into one of the equations, for example, the first equation: \(y = -2(\frac{12}{5}) + 7\)

Step 6 ：Simplify the expression: \(y = -\frac{24}{5} + \frac{35}{5}\)

Step 7 ：Add the fractions: \(y = \frac{11}{5}\)

Step 8 ：\(\boxed{(\frac{12}{5}, \frac{11}{5})}\)