Write a system of two equations in two variables to solve...

Write a system of two equations in two variables to solve each problem.
Investment Clubs. Part of $\$ 8,000$ was invested by an investment club at $10 \%$ interest and the rest at $12 \% .$ If the annual income from these investments is $\$ 900,$ how much was invested at each rate?

Key Concepts

System of Linear Equations

A system of linear equations consists of two or more equations involving the same set of variables where each equation represents a linear relationship. It allows for the simultaneous determination of the values of these variables that satisfy all of the equations, making it a fundamental tool in solving problems where multiple conditions must be met.

Defining Variables

Defining variables is the process of representing unknown quantities using symbols, typically letters. This is essential in translating real-world problems into mathematical terms, as it lays the groundwork for setting up equations that can model various relationships within the problem.

Translating Word Problems into Equations

Translating word problems into equations involves reading a narrative or description to identify the relationships between different quantities and then expressing these relationships in the form of algebraic equations. This skill is critical because it bridges the gap between real-life situations and mathematical solutions.

Interest Calculation in Investments

Interest calculation in investments involves determining the income earned based on the rate of interest applied to the invested amount. When different portions of a total amount are invested at different rates, establishing equations based on these rates enables one to calculate the overall return and allocate the investments accurately.

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