The of an equation is formed by all the points in the plane that make it true.

(a)

Step-by-step explanation:

Given the 2 equations

6x + 2y = - 6 → (1)

3x - 4y = - 18 → (2)

Multiplying (1) by 2 and adding to (2) will eliminate the term in y

12x + 4y = - 12 → (3)

Add (2) and (3) term by term

15x = - 30 ( divide both sides by 15 )

x = - 2

Substitute x = - 2 into either (1) or (2) and solve for y

Substituting into (1)

6(- 2) + 2y = - 6

- 12 + 2y = - 6 ( add 12 to both sides )

2y = 6 (divide both sides by 2 )

y = 3

Solution is (- 2, 3)

To determine the system with the same solution.

Substitute the x and y values of the solution into the left side of the equations and if equal to the right side then they are a solution.

(a)

8(- 2) + 4(3) = - 16 + 12 = - 4 = right side

17(- 2) + 2(3) = - 34 + 6 = - 28 = right side

Thus system (a) has the same solution