Final answer:
The solution to the system of equations 2x + 2y = -6 and 7x + y = 3 is found by rewriting the equations in slope-intercept form and graphing them. The lines intersect at the point (1, -4), which is the solution to the system.
Step-by-step explanation:
The system of equations to solve is 2x + 2y = -6 and 7x + y = 3. To solve by graphing, first rewrite both equations in slope-intercept form (y=mx+b).
For the first equation 2x + 2y = -6, if we solve for y, it becomes y = -x - 3. The slope is -1, and the y-intercept is -3.
For the second equation 7x + y = 3, if we solve for y, it becomes y = -7x + 3. Here, the slope is -7, and the y-intercept is 3.
Plot both lines on graph paper using their respective slopes and y-intercepts. The point where the two lines intersect is the solution to the system. Through graphing, we find that the lines intersect at the point (1, -4). Therefore, the correct answer to the system of equations is Option B: (1, -4).