17. \( 10 x+5 y=120 \)

To solve the equation \( 10x + 5y = 120 \), we can express it in terms of one variable or find specific values for \( x \) and \( y \). ### Step 1: Simplify the equation We can simplify the equation by dividing all terms by 5: \[ 2x + y = 24 \] ### Step 2: Solve for \( y \) Now, we can express \( y \) in terms of \( x \): \[ y = 24 - 2x \] ### Step 3: Find specific values We can choose specific values for \( x \) to find corresponding values of \( y \). 1. If \( x = 0 \): \[ y = 24 - 2(0) = 24 \quad \Rightarrow \quad (0, 24) \] 2. If \( x = 6 \): \[ y = 24 - 2(6) = 12 \quad \Rightarrow \quad (6, 12) \] 3. If \( x = 12 \): \[ y = 24 - 2(12) = 0 \quad \Rightarrow \quad (12, 0) \] ### Step 4: General solution The general solution for the equation \( 10x + 5y = 120 \) can be expressed as: \[ y = 24 - 2x \] This represents a line in the \( xy \)-plane, and any point \((x, y)\) that satisfies this equation is a solution. ### Conclusion The equation \( 10x + 5y = 120 \) can be simplified to \( y = 24 - 2x \), and you can find specific solutions by substituting different values for \( x \).