RCISE 5 Solve for \( x \) and \( y \) by using the method of substitution: \( \begin{array}{ll}\text { (1) } x-y=8 \text { and } 2 x+y=10 & \text { (2) } 3 x-y=2 \text { and } 7 x-2 y=8 \\ \text { (3) } 3 x+5 y=8 \text { and } x-2 y=-1 & \text { (4) } 7 x-3 y=41 \text { and } 3 x-y=17\end{array} \) Solve for \( x \) and \( y \) using either the elimination or substitution method: \( \begin{array}{ll}\text { (1) } x+y=1 \text { and } x-2 y=1 & \text { (2) } \\ \text { (3) } x+4 y=14 \text { and } 3 x+2 y=12 & \text { (4) } 2 y-3 x=7 \text { and } 4 y-5 x=21 \\ \text { (5) } 3 x+2 y=6 \text { and } 5 x+3 y=11 & \\ \text { (6) } \frac{y-2}{3}-\frac{x-1}{2}=1 \text { and } \frac{y-4}{5}-\frac{x-3}{4}=1 \\ \text { At ABC shop, } 3 \text { hamburgers and } 2 \text { cooldrinks cost R89, whereas } 2 \text { hamburgers and } \\ 3 \text { cooldrinks cost R73,50. Determine the cost of I hamburger. }\end{array} \)

To solve the system of equations using the method of substitution, start with the first equation from each set. For (1): From \( x - y = 8 \), we can express \( x \) as \( x = y + 8 \). Substitute this expression into the second equation, \( 2x + y = 10 \): \( 2(y + 8) + y = 10 \). Simplifying gives you \( 3y + 16 = 10 \), or \( 3y = -6 \), leading to \( y = -2 \). Substituting \( y \) back gives \( x = 6 \). For (2): Start with \( 3x - y = 2 \), or \( y = 3x - 2 \). Plug this into the second equation \( 7x - 2y = 8 \) to find \( x\) and then back-substitute to find \( y\). Now, let’s get cooking with real-world applications of these equations! You can think of systems of equations as a way to manage budgets, determine supplies, or even balance recipes! For instance, the hamburger and cool drink problem translates beautifully into practical budgeting—figuring out how much each item actually costs based on combined quantities. Perfect for any aspiring restaurateur or savvy shopper! If you're intrigued and want to dive deeper into the realm of algebra, picking up a good book on linear algebra can greatly enrich your understanding! Look for titles that break down the concepts with real-world scenarios—these are often easier to digest than lengthy theory-only texts. Videos and interactive resources can also provide engaging perspectives on systems of equations, making learning feel less like a chore and more like a challenge you can overcome.