Answer: X = —5 and Y = —2
Step-by-step explanation: What we have is a pair of simultaneous equations;
3X + Y = —17 —————-(1)
6X — 6Y = —18 ————(2)
We shall use the substitution method as instructed. Looking at equation (1),
We shall make Y the subject of the equation, hence
Y = —17 —3X
We shall now substitute for the value of Y into equation (2)
6X — 6Y = —18
6X — 6(—17 —3X) = —18
6X + 102 + 18X = —18
By collecting like terms we now have
24X = —18 —102
(Note that when a positive value crosses to the other side of the equation it becomes negative and vice versa)
24X = —120
Divide both sides of the equation by 24
X = —5
Having calculated the value of X as —5, we can now calculate Y as follows
From equation (1)
3X + Y = —17
3(—5) + Y = —17
—15 + Y = —17
Add 15 to both sides of the equation
—15 + 15 + Y = —17 + 15
Y = —2
Therefore, X = —5 and Y = —2