solve this problem---Question Stem: Solve the system of equations and find the value of x * y. Equations: x + y = 1 x - y = 0 Question: x * y = ?

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We have a system of two linear equations: x plus y equals 1, and x minus y equals 0. We need to find the value of x times y. Let's visualize this system graphically to understand the solution. Let's solve this system step by step using the elimination method. First, we add the two equations together to eliminate the variable y. When we add x plus y equals 1 and x minus y equals 0, the y terms cancel out, giving us 2x equals 1. Therefore, x equals one half. Now that we know x equals one half, we substitute this value into the first equation to find y. Substituting x equals one half into x plus y equals 1 gives us one half plus y equals 1. Solving for y, we get y equals 1 minus one half, which equals one half. Finally, we calculate the product x times y. We found that x equals one half and y equals one half. Therefore, x times y equals one half times one half, which equals one fourth. The answer is one fourth. Let's summarize our complete solution. We started with the system x plus y equals 1 and x minus y equals 0. Using elimination, we found x equals one half. By substitution, we found y equals one half. Therefore, x times y equals one fourth. We can verify our solution: one half plus one half equals 1, and one half minus one half equals 0. Both equations are satisfied, confirming our answer is correct.