Question
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\( \left. \begin{array} { r } { 10 s + 7 t = 69 } \\ { 4 s + 5 t = 43 } \\ { s = 2 , t = 7 } \end{array} \right. \)

Ask by Morrison Mills. in Pakistan
Feb 03,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

\( s = 2 \) and \( t = 7 \).

Solution

Solve the system of equations \( 10s+7t=69;4s+5t=43;s=2;t=7 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}10s+7t=69\\4s+5t=43\\s=2\\t=7\end{array}\right.\) - step1: Substitute the value of \(s:\) \(\left\{ \begin{array}{l}10\times 2+7t=69\\4\times 2+5t=43\\t=7\end{array}\right.\) - step2: Simplify: \(\left\{ \begin{array}{l}20+7t=69\\8+5t=43\\t=7\end{array}\right.\) - step3: Solve the equation: \(\left\{ \begin{array}{l}t=7\\8+5t=43\\t=7\end{array}\right.\) - step4: Substitute the value of \(t:\) \(\left\{ \begin{array}{l}8+5\times 7=43\\7=7\end{array}\right.\) - step5: Simplify: \(\left\{ \begin{array}{l}43=43\\7=7\end{array}\right.\) - step6: Calculate: \(\left\{ \begin{array}{l}s=2\\t=7\end{array}\right.\) - step7: Check the solution: \(\left\{ \begin{array}{l}s=2\\t=7\end{array}\right.\) - step8: Rewrite: \(\left(s,t\right) = \left(2,7\right)\) The solution to the system of equations is \( s = 2 \) and \( t = 7 \).

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The Deep Dive

Did you know that linear equations like these are the building blocks of algebra? This system of equations shows us how two variables, \( s \) and \( t \), can work together to find a solution that satisfies both equations. Solving such systems can help model real-world scenarios, like budgeting or resource allocation, where you need to find the best combination of different items or services! When trying to solve systems of equations, a common mistake is to misinterpret the coefficients or constant terms. Always double-check your calculations after substituting values back into the original equations to ensure they hold true. Keeping track of signs (positive/negative) is crucial, especially when dealing with multiple variables!

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