Question

Choose the one alternative that best completes the statement or answers the question.Solve the system graphically. If the system has an infinite number of solutions, use set-builder notation to write the solution set. If the system has no solution, state this.

1) 6x + y = -17
2)x + 3y = -17

A) (-4,7)
B) (-2, -3)
C) (-5)
D) (-2,-5)​

Answer 1

To solve the system graphically, plot both equations and find their point of intersection. The solution to the system of equations 6x + y = -17 and x + 3y = -17 is the point (-2, -5), which is option D).

Step-by-step explanation:

To solve the system graphically, we plot both equations on the same set of axes and look for their point of intersection, which represents the solution to the system.

1. For the first equation, 6x + y = -17, we can solve for y to get y = -6x - 17.
2. For the second equation, x + 3y = -17, we solve for y and get y = -(1/3)x - 17/3.
3. Plot both lines on the same graph. The point at which they intersect is the solution.

Using graphing techniques or solving the system algebraically by substituting x from one equation into the other, we can find that the solution is (-2, -5), which corresponds to option D).