Solve the following simultaneous equations using graphical method. (Use a grid paper to draw your graph) (6 marks) \[ y=4 x-5 \] \( y=-2 x+7 \)

To solve the given simultaneous equations graphically, start by plotting both lines on a grid. First, for the equation \(y = 4x - 5\), find two points to draw the line: when \(x = 0\), \(y = -5\) (point A: (0, -5)), and when \(x = 1\), \(y = -1\) (point B: (1, -1)). For the second equation \(y = -2x + 7\), select points as well: when \(x = 0\), \(y = 7\) (point C: (0, 7)), and when \(x = 3\), \(y = 1\) (point D: (3, 1)). Plot these points on the graph and draw straight lines through them. The intersection point of the two lines will give you the solution of the simultaneous equations! To find the exact point of intersection, you can also calculate it algebraically by setting the equations equal to each other: \(4x - 5 = -2x + 7\). Rearranging gives \(6x = 12\), so \(x = 2\). Substitute \(x = 2\) back into either equation to find \(y = 3\). Therefore, the solution is the point (2, 3). Remember, always label your axes and clearly mark the intersection point on your graph for clarity!