Question
1. \( \left\{\begin{array}{l}x+4 y=8 \\ 2 x+8 y=6\end{array}\right. \)
Ask by Simpson Bright. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The system of equations has no solution.
Solution
Solve the system of equations \( x+4y=8;2x+8y=6 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}x+4y=8\\2x+8y=6\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}x=8-4y\\2x+8y=6\end{array}\right.\)
- step2: Substitute the value of \(x:\)
\(2\left(8-4y\right)+8y=6\)
- step3: Simplify:
\(16=6\)
- 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 \( \begin{cases} x+4y=8 \\ 2x+8y=6 \end{cases} \) has no solution.
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Simplify this solution Extra Insights
To solve this system of equations, we can use the method of substitution or elimination. However, looking closely, we can see that the second equation is simply a multiple of the first equation (the first equation multiplied by 2 gives \(2x + 8y = 16\), which is different from the second equation \(2x + 8y = 6\)). This indicates that the two lines represented by these equations are parallel and will never intersect, therefore, there is no solution. Remember, when you encounter a system of equations that appears inconsistent, it’s always good to double-check the relationships between the equations to confirm they represent parallel lines or have no intersection points.
