Pregunta
2) \( \begin{array}{r}5 x-4 y=1 \\ x-y=-7\end{array} \)
Ask by Moreno Harmon. in Thailand
Mar 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The solution is \( x=29 \) and \( y=36 \).
Solución
Solve the system of equations \( 5x-4y=1;x-y=-7 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}5x-4y=1\\x-y=-7\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}5x-4y=1\\x=-7+y\end{array}\right.\)
- step2: Substitute the value of \(x:\)
\(5\left(-7+y\right)-4y=1\)
- step3: Simplify:
\(-35+y=1\)
- step4: Move the constant to the right side:
\(y=1+35\)
- step5: Add the numbers:
\(y=36\)
- step6: Substitute the value of \(y:\)
\(x=-7+36\)
- step7: Calculate:
\(x=29\)
- step8: Calculate:
\(\left\{ \begin{array}{l}x=29\\y=36\end{array}\right.\)
- step9: Check the solution:
\(\left\{ \begin{array}{l}x=29\\y=36\end{array}\right.\)
- step10: Rewrite:
\(\left(x,y\right) = \left(29,36\right)\)
The solution to the system of equations is \( (x,y) = (29,36) \).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Beyond the Answer
To solve the system of equations, we can use substitution or elimination. First, let's solve the second equation for \(x\): From \(x - y = -7\), we rearrange it to find \(x = y - 7\). Now, we can substitute this expression for \(x\) into the first equation: \[ 5(y - 7) - 4y = 1 \] Expanding this gives: \[ 5y - 35 - 4y = 1 \implies y - 35 = 1 \implies y = 36 \] Now, substitute \(y = 36\) back into \(x = y - 7\): \[ x = 36 - 7 = 29 \] So the solution to the system of equations is \(x = 29\) and \(y = 36\)! In conclusion, the pair \((x, y)\) is \((29, 36)\).
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