Question

L engore this text just here for 20 characters

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Answer 1

Option 4: (8,-12)

Explanation:

¼x - ½y = 8

x - 2y = 32

x = 32 + 2y

½x + ¾ = -5

2x + 3y = -20

2(32 + 2y) + 3y = -20

64 + 4y + 3y = -20

7y = -84

y = -12

x = 32 + 2(-12)

x = 8

Answer 2

Option D:

The solution to the system of equations is (8, –12).

Solution:

Given system of equations are

`$(1)/(4) x-(1)/(2) y=8` – – – – (1)

`$(1)/(2) x+(3)/(4) y=-5` – – – – (2)

Lets simplify these equations.

In equation (1), take LCM of the denominator and make the same.

`$(1)/(4) x-(2)/(4) y=8`

Do cross multiplication, we get

`x-2y=32`

Add 2y on both sides of the equations.

`x=32+2y` – – – – (3)

In equation (1), take LCM of the denominator and make the same.

`$(2)/(4) x+(3)/(4) y=-5`

Do cross multiplication, we get

`2x+3y=-20` – – – – (4)

Substitute equation (3) in (4), we get

`2(32+2y)+3y=-20`

`64+4y+3y=-20`

`64+7y=-20`

Subtract 64 from both sides of the equation.

`7y=-84`

Divide by –7 on both sides of the equation.

y = –12

Substitute y = –12 in equation (3).

`x=32+2(-12)`

`x=32-24`

x = 8

The solution to the system of equations is (8, –12).

Hence option D is the correct answer.