Question

Which BEST describes the system of equations? 3x = 5 - 4y 6x + 8y = 7 A) Consistent B) Inconsistent Consistent and Dependent D) Consistent and Independent

Answer 1

The given set of equations is,

`\begin{gathered} 3x=5-4y \\ \Rightarrow3x+4y-5=0\ldots\text{.}(1) \\ 6x+8y=7 \\ \Rightarrow6x+8y-7=0\ldots\ldots(2) \end{gathered}`

The ratio of coefficient can be determined as,

`\begin{gathered} (a_1)/(a_2)=(3)/(6)=(1)/(2)_{} \\ (b_1)/(b_2)=(4)/(8)=(1)/(2) \\ (c_1)/(c_2)=(-5)/(-7)=(5)/(7) \\ (a_1)/(a_2)=(b_1)/(b_2)\\e(c_1)/(c_2) \end{gathered}`

Thus, the solution is inconsistent as there is no solution.

Thus, option (B) is the correct solution.