Question

The equations were multiplied by constants and added together to determine that the value of x in the system of equations is –4. -3/4x=2/3y=-1 1/2x-5/6y=-7 What is the value of y? A. -6 B.-3 C. 3 D. 6

Answer 1

Option D is correct.

y =6

Explanation:

Given the system of equation:

`-(3)/(4)x-(2)/(3)y = -1` .......[1]

`(1)/(2)x-(5)/(6)y = -7` .......[2]

Multiply equation by 12 in [1] we get;

`-9x-8y = -12` .......[3]

Multiply equation by 12 in [2] we get;

`6x-10y = -84` .......[4]

Multiply equation [3] by 5 we get;

`-45x-40y = -60` .....[5]

Multiply equation [4] by 4 we get;

`24x-40y = -336` .....[6]

Subtract equation [6] from [5] to eliminate x we get;

`-69 x = 276`

Divide both sides by 69 we get;

x = -4

Substitute the value of x in [3] we get;

`-9(-4)-8y = -12`

`36-8y = -12`

Subtract 36 from both sides we get;

`-8y = -48`

Divide both sides by -8 we get;

y = 6

Therefore, the value of y is 6