Question

Describe the solution to the system of equations graphed below.

3x+y=-6
9x+3y=-18
27
OA The system has the unique solution (3, 4)
OB. The system has infinitely many solutions of the form y=-3x-6 where x is any real number
OC. The system has no solution
OD. The system has the unique solution (3, 18)

Answer 1

A.

The system has infinitely many solutions of the form y = -3x - 6 where x is any real number.

Explanation:

Answer 2

Answer is B. Infinitely many solutions

Step by step

Solve the equation

Change the first equation to y intercept form

y = -3x -6

Substitute it into the 2nd equation for y and solve

9x + 3(-3x-6) = -18

Distribution multiply

9x -9x -18 = -18

Add 18 to both sides to isolate x

9x -9x -18 + 18 = -18 + 18

Combine like terms

0 = 0

Since 0 = 0 for any value of x, the system of equations has infinite solutions.

Problem solved !!