EXPLANATION:
Given;
We are given the following system of equations;
[tex]\begin{gathered} -x+4y=10---(1) \\ \\ \frac{1}{2}x-2y=14---(2) \end{gathered}[/tex]
Required;
We are required to determine if the system of equations is dependent, independent or inconsistent.
Step-by-step solution;
We will start by taking equation (1). From this we make x the subject of the equation;
[tex]\begin{gathered} -x+4y=10 \\ \\ -x=10-4y \\ \\ Multiply\text{ }all\text{ }through\text{ }by\text{ }-1: \\ x=-10+4y \end{gathered}[/tex]
Next step is to substitute the value of x into equation (2);
[tex]\begin{gathered} \frac{1}{2}x-2y=14 \\ \\ \frac{1}{2}(-10+4y)-2y=14 \end{gathered}[/tex][tex]-5+2y-2y=14[/tex]
We now collect all like terms;
[tex]\begin{gathered} 2y-2y=14+5 \\ \\ 0=19 \end{gathered}[/tex]
This equation is not true since zero does not equal to 19.
Therefore;
ANSWER:
The equations are INCONSISTENT.
There is no solution based on our calculations above.
