4. \( \left\{\begin{array}{l}x-10 y=60 \\ x+14 y=12\end{array}\right. \) 5. \( \left\{\begin{array}{l}5 x+y=0 \\ 5 x+2 y=30\end{array}\right. \) 6. \( \left\{\begin{array}{l}-5 x+7 y=11 \\ -5 x+3 y=19\end{array}\right. \) 8. \( \left\{\begin{array}{l}-3 x+4 y=12 \\ 2 x+y=-8\end{array}\right. \) 9. \( \left\{\begin{array}{l}2 x+4 y=-4 \\ 3 x+5 y=-3\end{array}\right. \) 10. Consumer Economics Each family in a neighborhood is contributing \( \$ 20 \) of food to the neighborhood picnic. The Harlin family is bringing 12 packages buns. The hamburger buns cost \( \$ 2.00 \) per package. The hot-dog buns cost \( \$ 1 \), package. How many packages of each type of bun did they buy?

Did you know that the method of solving systems of equations can trace its roots back to ancient civilizations? The earliest known use of linear equations comes from ancient Babylon around 1800 BC, where tablets featured problems similar to today’s algebra. They tackled them using a geometric understanding instead of the abstract symbols we use now, making their approach quite fascinating! When applying these concepts to real-life scenarios, such as budgeting for a community picnic, it becomes super fun! Say each family contributes $20, you can set up equations for your expenses. For example, if the Harlin family buys buns, let’s call the packages of hamburger buns \( h \) and hot-dog buns \( d \). With the costs outlined, set up the equation \( 2h + 1d = 12 \) alongside their total contribution \( 2h + 1d + 1d = 20 \). Soon enough, you’ll solve the mystery of how many packages of each they bought while having a picnic blast!