Graph the system below and write its solution. \[ \begin{array}{c}3 x+y=5 \\ y=-\frac{1}{3} x-3\end{array} \] Note that you can also answer "No solution" or "Infinitely many"

To graph the system of equations, let's first rewrite both equations in slope-intercept form (y = mx + b). 1. The first equation \(3x + y = 5\) can be rewritten as: \[ y = -3x + 5 \] This represents a line with a slope of -3 and a y-intercept at (0, 5). 2. The second equation \(y = -\frac{1}{3}x - 3\) is already in slope-intercept form. This line has a slope of -\(\frac{1}{3}\) and a y-intercept at (0, -3). Now, we can graph these two lines: - Plot the first line starting at (0, 5) and using the slope to move down 3 units for each 1 unit you move right. - For the second line, plot it starting at (0, -3) and using the slope to move down 1 unit for every 3 units you move to the right. After graphing, you will see that the lines intersect. To find the solution, solve the system of equations. Set the two expressions for \(y\) equal: \[ -3x + 5 = -\frac{1}{3}x - 3 \] Multiply through by 3 to eliminate the fraction: \[ -9x + 15 = -x - 9 \] Combine like terms: \[ -8x = -24 \] \[ x = 3 \] Substitute \(x = 3\) back into one of the original equations to find \(y\): \[ y = -3(3) + 5 = -9 + 5 = -4 \] So the solution to the system is: \[ (x, y) = (3, -4) \]