Use the diagram to work out the solution to these simultaneous equations:
\[
\begin{array}{l}
y=-2 x+7 \\
y=\frac{1}{2} x+1
\end{array}
\]
Answer
\(\boxed{(\frac{12}{5}, \frac{11}{5})}\)
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 ：\(\boxed{(\frac{12}{5}, \frac{11}{5})}\)
