Answer:
A. (–8, 2)
Step-by-step explanation:
The given system is
[tex]y=\frac{1}{2}x+6\\ y=-\frac{3}{4}x-4[/tex]
Let us equate both of them to get:
[tex]\frac{1}{2}x+6=-\frac{3}{4}x-4[/tex]
Multiply through by 4 to get:
[tex]4*\frac{1}{2}x+4*6=4*-\frac{3}{4}x-4*4[/tex]
Simplify:
[tex]2x+24=-3x-16[/tex]
Group similar terms:
[tex]2x+3x=-16-24\\5x=-40\\x=-8[/tex]
Put x=-8 in the first equation:
[tex]y=\frac{1}{2}(-8)+6=-4+6=2[/tex]
The correct answer is A
