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\( x=4 \), \( y=5 \)
Solución
Solve the system of equations \( 2x-y=3;y=9-x \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}2x-y=3\\y=9-x\end{array}\right.\)
- step1: Substitute the value of \(y:\)
\(2x-\left(9-x\right)=3\)
- step2: Simplify:
\(3x-9=3\)
- step3: Move the constant to the right side:
\(3x=3+9\)
- step4: Add the numbers:
\(3x=12\)
- step5: Divide both sides:
\(\frac{3x}{3}=\frac{12}{3}\)
- step6: Divide the numbers:
\(x=4\)
- step7: Substitute the value of \(x:\)
\(y=9-4\)
- step8: Simplify:
\(y=5\)
- step9: Calculate:
\(\left\{ \begin{array}{l}x=4\\y=5\end{array}\right.\)
- step10: Check the solution:
\(\left\{ \begin{array}{l}x=4\\y=5\end{array}\right.\)
- step11: Rewrite:
\(\left(x,y\right) = \left(4,5\right)\)
The solution to the system of equations \(2x-y=3\) and \(y=9-x\) is \(x=4\) and \(y=5\).
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Simplifique esta solución Bonus Knowledge
Let’s dive into the history of equations! Linear equations like the ones you provided date back to ancient mathematicians such as the Babylonians. They used geometric methods to solve problems that can be represented by equations today. Over centuries, these concepts evolved, giving rise to the algebraic techniques we use now! Now, for a real-world application: Consider using these equations to model a budget scenario! The first equation might represent a constraint on spending, while the second could signify a limit on savings. Solving these equations helps you analyze financial decisions, ensuring that both your spending and savings work together harmoniously!
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