Solve the system of equations . 6x-3y=-6, 9x-3y=-18

Answer 1

To solve the given system of linear equations:

1. \(6x - 3y = -6\)
2. \(9x - 3y = -18\)

We can use the elimination method to find the values of \(x\) and \(y\). Start by subtracting the first equation from the second equation:

\[ (9x - 3y) - (6x - 3y) = -18 - (-6) \]

Simplifying this, we get:

\[ 9x - 3y - 6x + 3y = -18 + 6 \]
\[ 3x = -12 \]

Next, solve for \(x\):

\[ x = \frac{-12}{3} \]
\[ x = -4 \]

Now substitute \(x = -4\) back into the first equation to solve for \(y\):

\[ 6(-4) - 3y = -6 \]
\[ -24 - 3y = -6 \]

Isolate \(y\):

\[ -3y = -6 + 24 \]
\[ -3y = 18 \]
\[ y = \frac{18}{-3} \]
\[ y = -6 \]

So the solution to the system of equations is \( x = -4 \) and \( y = -6 \). You can check this solution by substituting \(x\) and \(y\) back into the original equations to verify that both are satisfied.

For the first equation:
\[ 6(-4) - 3(-6) = -6 \]
\[ -24 + 18 = -6 \]
\[ -6 = -6 \] (True)

For the second equation:
\[ 9(-4) - 3(-6) = -18 \]
\[ -36 + 18 = -18 \]
\[ -18 = -18 \] (True)

Therefore, the solution to the system of equations is \( x = -4 \) and \( y = -6 \).