Pregunta
What is the solution to the system of equations? \( \left\{\begin{array}{l}-4 x-10 y=-12 \\ 2 x+5 y=-3\end{array}\right. \)
Ask by Wells Mullins. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The system of equations has no solution.
Solución
Solve the system of equations \( -4x-10y=-12;2x+5y=-3 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}-4x-10y=-12\\2x+5y=-3\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}x=\frac{6-5y}{2}\\2x+5y=-3\end{array}\right.\)
- step2: Substitute the value of \(x:\)
\(2\times \frac{6-5y}{2}+5y=-3\)
- step3: Simplify:
\(6=-3\)
- step4: Calculate:
\(\left\{ \begin{array}{l}x \in \varnothing \\y \in \varnothing \end{array}\right.\)
- step5: Rewrite:
\((x, y) \in \varnothing\)
The system of equations \( \left\{\begin{array}{l}-4 x-10 y=-12 \\ 2 x+5 y=-3\end{array}\right. \) has no solution.
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Simplifique esta solución Extra Insights
To solve the system of equations, we can use the method of elimination or substitution. If we take the second equation, \(2x + 5y = -3\), and multiply it by 2, we can align it with the first equation: \[ 4x + 10y = 6 \] Now, we can add this to the first equation: \[ -4x - 10y = -12 \] \[ 4x + 10y = 6 \] Adding them cancels out \(x\) and \(y\): \[ 0 = -6 \] This is a contradiction, which means the system of equations has no solutions. The lines represented by these equations are parallel and never intersect.
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