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\begin{tabular}{l|l}\( \begin{array}{l}\text { Solve these simultaneous } \\ \text { equations using a graphical }\end{array} \) & Tip \\ method. & \( \begin{array}{l}\text { Rearrange both equations to make } y \text { the subject } \\ \text { then draw tables of values for } x=0,2 \text { and } 4 . \\ 3 x+y=8\end{array} \) \\ \hline\end{tabular}

Ask by Chadwick Harper. in Egypt
Jan 22,2025

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To solve the system of equations graphically, rearrange both equations to solve for \( y \), create tables of values for \( x = 0, 2, 4 \), plot the lines, and find their intersection point. For the given example: 1. \( y = -3x + 8 \) 2. \( y = \frac{1}{2}x - 2 \) Plotting these lines shows they intersect at \( \left( \frac{20}{7}, -\frac{4}{7} \right) \).

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Beyond the Answer

To solve the equation \(3x + y = 8\) for \(y\), we rearrange it to get \(y = 8 - 3x\). Now, by substituting \(x\) values of 0, 2, and 4, we can find the corresponding \(y\) values: - For \(x = 0\), \(y = 8 - 3(0) = 8\) - For \(x = 2\), \(y = 8 - 3(2) = 2\) - For \(x = 4\), \(y = 8 - 3(4) = -4\) Plot these points \((0,8)\), \((2,2)\), and \((4,-4)\) on a graph and connect them to visualize the line. Now, once you have one equation in graphical form, try the same process for a second equation. This allows you to identify the point of intersection where both lines meet; that point will be your solution to the simultaneous equations.

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