Asked by Royal Guardian on May 09, 2024
Verified
Decide whether the system {5x−6y=4−15x+18y=14\left\{ \begin{array} { c } 5 x - 6 y = 4 \\- 15 x + 18 y = 14\end{array} \right.{5x−6y=4−15x+18y=14 is consistent or inconsistent.
A) inconsistent
B) consistent
Consistent
In the context of systems of equations, it describes a system that has at least one solution.
Inconsistent
A term used to describe a system of equations that has no solution because the equations represent parallel lines.
- Examine the uniformity in systems of equations.
Verified Answer
SB
Shauna BohrenMay 15, 2024
Final Answer :
A
Explanation :
To solve this system, we can multiply the first equation by 3 to get:
15x−18y=12−15x+18y=14\begin{align*}15x - 18y &= 12 \\-15x + 18y &= 14\end{align*}15x−18y−15x+18y=12=14
Adding the two equations together, we get:
0=26\begin{align*}0 &= 26\end{align*}0=26
This is a contradiction, so the system is inconsistent. The answer is A.
15x−18y=12−15x+18y=14\begin{align*}15x - 18y &= 12 \\-15x + 18y &= 14\end{align*}15x−18y−15x+18y=12=14
Adding the two equations together, we get:
0=26\begin{align*}0 &= 26\end{align*}0=26
This is a contradiction, so the system is inconsistent. The answer is A.
Learning Objectives
- Examine the uniformity in systems of equations.
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