Pregunta
Solve. \[ \begin{array}{l}-9 x-3 y=6 \\ -7 x-5 y=18\end{array} \]
Ask by Griffiths Goodwin. in the United States
Feb 28,2025
Solución de inteligencia artificial de Upstudy
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The solution is \( x = 1 \) and \( y = -5 \).
Solución
We are given the system of equations:
-9x - 3y = 6
-7x - 5y = 18
Step 1. Multiply the first equation by 5 and the second equation by 3 to eliminate y:
(1) × 5: -45x - 15y = 30
(2) × 3: -21x - 15y = 54
Step 2. Subtract the second new equation from the first:
(-45x - 15y) - (-21x - 15y) = 30 - 54
-45x + 21x = -24
-24x = -24
Step 3. Solve for x:
x = (-24) / (-24) = 1
Step 4. Substitute x = 1 into one of the original equations. Using the first one:
-9(1) - 3y = 6
-9 - 3y = 6
-3y = 6 + 9
-3y = 15
y = 15 / (-3) = -5
The solution to the system is:
x = 1, y = -5
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To solve the system of equations: 1. From the first equation: \(-9x - 3y = 6\) Rearranging gives: \(-3y = 9x + 6\) Dividing by -3: \(y = -3x - 2\) 2. Substitute this expression for \(y\) into the second equation: \(-7x - 5(-3x - 2) = 18\) Simplifying: \(-7x + 15x + 10 = 18\) Combine like terms: \(8x + 10 = 18\) Subtracting 10 from both sides: \(8x = 8\) Therefore: \(x = 1\) 3. Now substitute \(x = 1\) back into the expression for \(y\): \(y = -3(1) - 2 = -3 - 2 = -5\) The solution to the system of equations is: \((x, y) = (1, -5)\)
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