Graph the system below and write its solution. \( \left\{\begin{array}{l}-2 x+y=6 \\ y=\frac{1}{2} x+3\end{array}\right. \)

To graph the system of equations and find its solution, we can follow these steps: 1. Graph the first equation \( -2x + y = 6 \) on a coordinate plane. 2. Graph the second equation \( y = \frac{1}{2}x + 3 \) on the same coordinate plane. 3. Find the point of intersection of the two lines, which will be the solution to the system of equations. Let's start by graphing the first equation \( -2x + y = 6 \). We can rewrite this equation in slope-intercept form as \( y = 2x + 6 \). The slope of this line is 2, and the y-intercept is 6. Next, let's graph the second equation \( y = \frac{1}{2}x + 3 \). The slope of this line is 1/2, and the y-intercept is 3. Now, we need to find the point of intersection of these two lines. To do this, we can set the two equations equal to each other and solve for x. Setting the two equations equal to each other, we have: \[ 2x + 6 = \frac{1}{2}x + 3 \] Solving for x, we get: \[ 2x - \frac{1}{2}x = 3 - 6 \] \[ \frac{3}{2}x = -3 \] \[ x = -2 \] Substituting x = -2 into one of the original equations, we can find the corresponding value of y. Let's use the first equation: \[ -2(-2) + y = 6 \] \[ 4 + y = 6 \] \[ y = 2 \] Therefore, the solution to the system of equations is \( (-2, 2) \).