EXPLANATION:
To get the solution of the simultaneous equation, using the elimination method:
We will have the following steps:
Step 1:
Write the two equations:
[tex]\begin{gathered} y=-\frac{1}{2}x+3 \\ y=-\frac{7}{2}x-3 \end{gathered}[/tex]
Step2: Subtract the two equations:
[tex]\begin{gathered} y-y=-\frac{1}{2}x-(-\frac{7}{2}x)+3-(-3) \\ 0=-\frac{1}{2}x+\frac{7}{2}x+6 \\ \end{gathered}[/tex]
Step 3: Simplify the expression
[tex]\begin{gathered} 0=3x+6 \\ 3x=-6 \\ x=-\frac{6}{3} \\ x=-2 \end{gathered}[/tex]
Step 4: Substitute x=-2 into the formula:
[tex]\begin{gathered} y=-\frac{1}{2}x+3 \\ y=-\frac{1}{2}\times-2+3 \\ y=1+3 \\ y=4 \end{gathered}[/tex]
Therefore, the answer is
[tex](-2,4)[/tex]
Thus,
Option B is correct
