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10) \( \begin{aligned}-5 x+y & =-3 \\ 3 x-8 y & =24\end{aligned} \)

Ask by Rowe Sandoval. in the United States
Jan 23,2025

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The solution is \( x=0 \) and \( y=-3 \).

Solución

Solve the system of equations \( -5x+y=-3;3x-8y=24 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-5x+y=-3\\3x-8y=24\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}y=-3+5x\\3x-8y=24\end{array}\right.\) - step2: Substitute the value of \(y:\) \(3x-8\left(-3+5x\right)=24\) - step3: Simplify: \(-37x+24=24\) - step4: Move the constant to the right side: \(-37x=24-24\) - step5: Subtract the terms: \(-37x=0\) - step6: Change the signs: \(37x=0\) - step7: Rewrite the expression: \(x=0\) - step8: Substitute the value of \(x:\) \(y=-3+5\times 0\) - step9: Simplify: \(y=-3\) - step10: Calculate: \(\left\{ \begin{array}{l}x=0\\y=-3\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=0\\y=-3\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(0,-3\right)\) The solution to the system of equations is \( (x,y) = (0,-3) \).

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Bonus Knowledge

To solve the system of equations \(-5x + y = -3\) and \(3x - 8y = 24\), we can start by expressing \(y\) from the first equation. From \(-5x + y = -3\), we get \(y = 5x - 3\). Now, substitute \(y\) into the second equation: \[ 3x - 8(5x - 3) = 24 \] This simplifies to: \[ 3x - 40x + 24 = 24 \implies -37x + 24 = 24 \implies -37x = 0 \implies x = 0. \] Now, substitute \(x = 0\) back into the expression for \(y\): \[ y = 5(0) - 3 = -3. \] Thus, the solution to the system of equations is \(x = 0\) and \(y = -3\), or as an ordered pair, \((0, -3)\).

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