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7. \( \left\{\begin{array}{l}x-3 y=-24 \\ 5 x+8 y=-5\end{array}\right. \)

Ask by Wagner Wright. in the United States
Feb 18,2025

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\( x = -9 \) and \( y = 5 \).

Solución

Solve the system of equations \( x-3y=-24;5x+8y=-5 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x-3y=-24\\5x+8y=-5\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=-24+3y\\5x+8y=-5\end{array}\right.\) - step2: Substitute the value of \(x:\) \(5\left(-24+3y\right)+8y=-5\) - step3: Simplify: \(-120+23y=-5\) - step4: Move the constant to the right side: \(23y=-5+120\) - step5: Add the numbers: \(23y=115\) - step6: Divide both sides: \(\frac{23y}{23}=\frac{115}{23}\) - step7: Divide the numbers: \(y=5\) - step8: Substitute the value of \(y:\) \(x=-24+3\times 5\) - step9: Calculate: \(x=-9\) - step10: Calculate: \(\left\{ \begin{array}{l}x=-9\\y=5\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=-9\\y=5\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(-9,5\right)\) The solution to the system of equations is \( x = -9 \) and \( y = 5 \).

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To solve the system of equations, let's first express the first equation in terms of \(x\): 1. From \(x - 3y = -24\), we can rewrite it as \(x = 3y - 24\). Now, substitute \(x\) in the second equation: 2. Substitute into \(5x + 8y = -5\): \[ 5(3y - 24) + 8y = -5 \\ 15y - 120 + 8y = -5 \\ 23y - 120 = -5 \\ 23y = 115 \\ y = 5 \] Now, substitute \(y\) back to find \(x\): 3. Using \(y = 5\) in \(x = 3y - 24\): \[ x = 3(5) - 24 = 15 - 24 = -9 \] Thus, the solution to the system is \(x = -9\) and \(y = 5\). The solution is \((x, y) = (-9, 5)\).

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