Find the point of intersection between the lines \( -8 x+4 y=-12 \) and \( -3 x-2 y=-28 \) using algebra. Write your answer as an ordered pair. If the lines do not intersect, enter DNE. Answer 2 Points Prev Keyboard Shortcuts

To find the point of intersection of the lines \( -8x + 4y = -12 \) and \( -3x - 2y = -28 \), we can solve these equations simultaneously. First, we can simplify both equations. For the first equation, dividing everything by 4 gives us: \[ -2x + y = -3 \quad \text{(Equation 1)} \] For the second equation, dividing everything by -1 gives us: \[ 3x + 2y = 28 \quad \text{(Equation 2)} \] Now, we can express \( y \) from Equation 1: \[ y = 2x - 3 \] Next, we substitute \( y \) into Equation 2: \[ 3x + 2(2x - 3) = 28 \] Simplifying this: \[ 3x + 4x - 6 = 28 \\ 7x - 6 = 28 \\ 7x = 34 \\ x = \frac{34}{7} \] Now we can find \( y \) using \( x \): \[ y = 2\left(\frac{34}{7}\right) - 3 \\ y = \frac{68}{7} - \frac{21}{7} \\ y = \frac{47}{7} \] Thus, the point of intersection is: \[ \left(\frac{34}{7}, \frac{47}{7}\right) \] So the ordered pair is: \( \left( \frac{34}{7}, \frac{47}{7} \right) \).