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

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Answer

$(\frac{12}{5}, \frac{11}{5})$

Steps

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

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 ： $(\frac{12}{5}, \frac{11}{5})$