Make use of the space provided to show all working out. QUESTION 1 Solve the following simultaneous equations using graphical method. (Use a grid paper to draw your graph) \[ \begin{array}{l}\text { (6 marks) } \\ \qquad y=4 x-5 \\ \qquad y=-2 x+7\end{array} \]

To solve the simultaneous equations graphically, you can follow these steps: First, rearrange the equations into slope-intercept form, which they already are! The first equation, \(y = 4x - 5\), has a slope of 4 and a y-intercept of -5. The second equation, \(y = -2x + 7\), has a slope of -2 and a y-intercept of 7. Now, plot both equations on a grid: for \(y = 4x - 5\), start from the point (0, -5) and use the slope to find additional points, e.g., (1, -1). For \(y = -2x + 7\), start from (0, 7) and find points such as (1, 5). Now, once you have the two lines plotted, look for the intersection point on your graph, which is the solution to the simultaneous equations. You’ll find that they intersect at one point, indicating the values of \(x\) and \(y\) that satisfy both equations—this is the graphical solution! Now, as you explore the graphical method, keep in mind that each line's slope and direction provide insights into the relationship between the two equations. Often, a gently sloped line might indicate less variance in output for changes in input. A steep slope, conversely, suggests a quicker change in output. This visual representation makes understanding how equations interact much easier and more intuitive! If you want to delve deeper, consider learning about the intersection of lines in different contexts, like economics or physics, where such equations can model real-life scenarios. This can give you a greater appreciation for why finding these intersecting points is vital in various fields! It’s always fascinating to see the practical implications of something as abstract as algebra!