Answer:
Option D: (8, -12) is the solution set for given system.
Explanation:
Given that:
1/4x-1/2y=8 ----------- eq1
1/2x+3/4y=-5 --------- eq2
Multiplying eq1 by 2 we get:
1/2x - y = 16 ------- eq3
Now by subtracting eq3 from eq2 we get:
(1/2x+3/4y) - (1/2x - y ) = -5 -16
By simplifying:
3/4y + y = -21
By taking LCM to make denominator same:
3/4y + y*4/4 = -21
3+4 / 4y = -21
7/4y = -21
Multiplying both sides by 4/7 we get
y = -21 * 4/7
y = -12
Putting value of y in eq3
1/2x - (-12)= 16
1/2x + 12 = 16
1/2x = 16 - 12
1/2x = 4
Multiplying both sides by 2
x = 4*2
x = 8
So the solution set = (8, -12)
i hope it will help you!