$182 = 2ZY + 6WY$
$95 = 2ZY + 2WY$
According to my solution and even an online calculator $Y$ equals to $3.625$ if $W = 6$ but if I plug in to the equations it doesn't give the correct answer. I have no idea what is wrong.
give that $Z=W-1$ therefore $182 = 2WY - 2Y +6WY$ and $95 = 2WY - 2Y +2WY$
On
Alternatively for the reader that is not familiar with subtracting equations, we could use substitution: $$ 2ZY + 6WY =182\tag{1}$$ $$ 2ZY + 2WY=95 \tag{2}$$ $$W=Z+1 \tag{3} $$
We first isolate $Y$: $$ Y(2Z + 6W) =182$$ $$ Y (2Z + 2W)=95 $$ $$W=Z+1 $$
We now use the third equation to simplify for $W$:
$$ Y(2Z + 6(Z+1)) =182$$ $$ Y (2Z + 2(Z+1))=95 $$ We simplify some more: $$ Y(8Z+6) =182$$ $$ Y (4Z + 2)=95 $$ We expand the brackets again: $$ 8YZ+6Y =182$$ $$ 4YZ + 2Y=95 $$ So we may also write that: $$ 8YZ+6Y =182$$ $$ 8YZ + 4Y=190 $$ So this also means that if we bring a term of $6Y$ to the other side: $$ 8YZ=182-6Y$$ $$ 8YZ + 4Y=190 $$ We then substitute the upper expression for $8YZ$ into the lower equation: $$ (182-6Y)+ 4Y = 190 $$
So now, after simplification and some algebra:
$$-2Y=8 \rightarrow Y=-4. $$
We start with the system of equations: $$ 2ZY + 6WY =182\tag{1}$$ $$ 2ZY + 2WY=95 \tag{2}$$
Subtract $(2)$ from the upper equation $(1)$ to get:
$$4WY=87$$ Subtract $(2)$ three times from $(1)$ to get: $$-4ZY=-103$$
We now use that $W=Z+1$ and rewrite the upper equation:
$$4(Z+1)Y=87$$ $$-4ZY=-103$$ We then proceed by distributivity and notice a common term in both equations:
$$4ZY+4Y=87$$ $$-4ZY=-103$$
Now we add these two equations again to cancel the factor of $4ZY$:
$$4Y= -16 \rightarrow Y=-4$$ We now can find the other variables quite easily from $$4WY=87 \rightarrow W=-\frac{87}{16}$$ $$4ZY=103\rightarrow Z=-\frac{103}{16}$$
Also see wolfram alpha: