Question
Solve the system of equations by any method. \[ -x+2 y=-1 \] \[ 7 x-14 y=8 \] Enter the exact answer as an ordered pair, \( (x, y) \)
Ask by Ramos Wheeler. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There is no solution; no ordered pair \( (x, y) \) satisfies both equations.
Solution
Solve the system of equations \( -x+2y=-1;7x-14y=8 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}-x+2y=-1\\7x-14y=8\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}x=1+2y\\7x-14y=8\end{array}\right.\)
- step2: Substitute the value of \(x:\)
\(7\left(1+2y\right)-14y=8\)
- step3: Simplify:
\(7=8\)
- 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 does not have a solution. Therefore, there is no ordered pair \( (x, y) \) that satisfies both equations.
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Simplify this solution The Deep Dive
To solve the system of equations, we can start with the first equation: \[-x + 2y = -1.\] We can rearrange it to express \( x \) in terms of \( y \): \[ x = 2y + 1. \] Next, substitute this expression into the second equation: \[ 7(2y + 1) - 14y = 8. \] Now distribute \( 7 \): \[ 14y + 7 - 14y = 8. \] Simplifying this, we get: \[ 7 = 8. \] This is a contradiction, which means that the system of equations has no solution. Therefore, the system is inconsistent. So the solution is: \[ \text{No solution (inconsistent system)}. \]
