Pregunta
2 Find the solution to the system of equations by \( y=6 \) \( 6 x-2 y=12 \) (A) \( (0,6) \)
Ask by Collins May. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The solution to the system of equations is \( (4, 6) \).
Solución
To solve the system of equations:
1. \( y = 6 \)
2. \( 6x - 2y = 12 \)
**Step 1: Substitute \( y = 6 \) into the second equation.**
\[
6x - 2(6) = 12
\]
\[
6x - 12 = 12
\]
**Step 2: Solve for \( x \).**
\[
6x = 12 + 12
\]
\[
6x = 24
\]
\[
x = \frac{24}{6} = 4
\]
**Solution:**
The solution to the system of equations is \( (4, 6) \).
**Verification:**
1. Substitute \( x = 4 \) and \( y = 6 \) into the first equation:
\[
y = 6 \quad \text{(True)}
\]
2. Substitute \( x = 4 \) and \( y = 6 \) into the second equation:
\[
6(4) - 2(6) = 24 - 12 = 12 \quad \text{(True)}
\]
**Conclusion:**
The correct solution is \( (4, 6) \). The option \( (0, 6) \) provided as (A) is **incorrect**.
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Simplifique esta solución Bonus Knowledge
To solve the system of equations, start with the first equation \( y = 6 \) and substitute it into the second equation. This gives: \( 6x - 2(6) = 12 \). This simplifies to: \( 6x - 12 = 12 \). Now, add 12 to both sides: \( 6x = 24 \). Divide both sides by 6 to find \( x \): \( x = 4 \). So the solution to the system of equations is \( (4, 6) \), not \( (0, 6) \)! One common mistake in systems of equations is not substituting correctly, which can lead to wrong results. Always double-check substitutions before moving on with further calculations. It’s also wise to verify the solution by plugging both values back into the original equations!
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