Question: The image shows a coordinate plane with a grid ranging from -10 to 10 on both the x-axis and…

The image shows a coordinate plane with a grid ranging from -10 to 10 on both the x-axis and y-axis. There are two equations displayed at the bottom of the image:

1. \( x - 3y = -6 \) (in orange)
2. \( y = -\frac{5}{3}x - 4 \) (in blue)

Below the equations, there is a prompt that reads: “The solution is (\(\\), \(\\))“. There is also a “Submit” button at the bottom.

Solution

To solve the system of equations: \[ \begin{cases} x - 3y = -6 & \\ y = -\frac{5}{3}x - 4 & \end{cases} \] Substitute the expression for \(y\) from the second equation into the first equation: \[ x - 3\left(-\frac{5}{3}x - 4\right) = -6 \] Distribute the \(-3\) through the parentheses: \[ x + 5x + 12 = -6 \] Combine like terms: \[ 6x + 12 = -6 \] Subtract 12 from both sides: \[ 6x = -18 \] Divide both sides by 6: \[ x = -3 \] Substitute \(x = -3\) into the equation for \(y\): \[ y = -\frac{5}{3}(-3) - 4 \] Calculate \(y\): \[ y = 5 - 4 \] \[ y = 1 \] The solution is \((-3, 1)\).