8) \( \begin{array}{l}5 x+3 y=10 \\ 4 x-2 y=8\end{array} \)

To solve the system of equations, start with the first equation \( 5x + 3y = 10 \). You can express \( y \) in terms of \( x \): \[ 3y = 10 - 5x \] \[ y = \frac{10 - 5x}{3} \] Now substitute this expression for \( y \) into the second equation \( 4x - 2y = 8 \): \[ 4x - 2\left(\frac{10 - 5x}{3}\right) = 8 \] Multiply through by 3 to eliminate the fraction: \[ 12x - 2(10 - 5x) = 24 \] \[ 12x - 20 + 10x = 24 \] \[ 22x - 20 = 24 \] Now solve for \( x \): \[ 22x = 44 \] \[ x = 2 \] Substituting \( x = 2 \) back into the equation for \( y \): \[ y = \frac{10 - 5(2)}{3} = \frac{10 - 10}{3} = 0 \] The solution to the system of equations is \( (x, y) = (2, 0) \). Now let's add some engaging context! The world of equations isn't just numbers—it’s a treasure hunt! Each equation is like a clue leading you to the hidden treasure, or in this case, the solution. Imagine you’re a detective piecing together evidence—each step brings you closer to crack the case! The solution \( (2, 0) \) is your "Aha!" moment, confirming that in this mystery, two is your answer while y hangs out with the zeros! Thinking about how this applies in real life? Think of it like coordinating schedules—two friends want to meet at the same time. Each schedule represents an equation, and by solving it, you find the perfect time (our solution!) to gather everyone! Whether it’s planning a road trip or balancing a budget, these equations help us find harmony in the chaos of everyday life!