Question

6x - 3y = -18\
-2x + 4y = 18 ( , )

Explanation:

Step1: Simplify the first equation

Divide the first equation \(6x - 3y=-18\) by 3, we get \(2x - y=-6\), which can be rewritten as \(y = 2x + 6\).

Step2: Substitute into the second equation

Substitute \(y = 2x + 6\) into the second equation \(-2x + 4y = 18\), we have:
\(-2x + 4(2x + 6)=18\)
Expand the left side: \(-2x + 8x + 24 = 18\)
Combine like terms: \(6x + 24 = 18\)
Subtract 24 from both sides: \(6x = 18 - 24=-6\)
Divide both sides by 6: \(x=\frac{-6}{6}=-1\)

Step3: Find the value of y

Substitute \(x = -1\) into \(y = 2x + 6\), we get \(y = 2\times(-1)+6=-2 + 6 = 4\)

Answer:

\((-1, 4)\)