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

Answer:

Option D is correct.

y =6

Step-by-step explanation:

Given the system of equation:

$-\frac{3}{4}x-\frac{2}{3}y = -1$           .......[1]

$\frac{1}{2}x-\frac{5}{6}y = -7$            .......[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