To find the point where the two equations intersect, we can solve the system of equations. The equations are:
- \(4x - 2y = -2\)
- \(12x - 3y = 9\)
We can simplify the second equation first by dividing all terms by 3:
\[ 4x - y = 3 \]
Now we have the two equations:
- \(4x - 2y = -2\)
- \(4x - y = 3\)
Next, we can solve for \(y\) in terms of \(x\) from the second equation:
\[ 4x - y = 3 \implies y = 4x - 3 \]
Now, we can substitute this expression for \(y\) back into the first equation:
\[ 4x - 2(4x - 3) = -2 \]
Simplifying this:
\[ 4x - 8x + 6 = -2 \] \[ -4x + 6 = -2 \] \[ -4x = -2 - 6 \] \[ -4x = -8 \] \[ x = 2 \]
Now, substitute \(x = 2\) back into the equation for \(y\):
\[ y = 4(2) - 3 = 8 - 3 = 5 \]
So the intersection point of the two equations is:
\((x, y) = (2, 5)\)
Therefore, when graphed, the two linear equations intersect at the point (2, 5).