The solution of two linear equations is (-2,2). one equations has a slope of 3. the slope of the other equation is the negative reciprocal of the slope of the first.

the system described above is represented by the following equations.

Its true ⇒ answer (a)

Step-by-step explanation:

* The solution of two linear equation means that this solution

  is a solution for each equation

* To check if the point is a solution of an equation

- Substitute its coordinates in the equation, if the left hand side

 is equal the right hand side, then the point is a solution

 of this equation

* Lets study our problem

- (-2 2) is the solution of two linear equations

- The slope of one equation is 3

- The slope of the second equation is the negative reciprocal

 of the slope of the first, means = -1/3

* Check the this conditions in the given equations

- In the equation y = 3x + 8 ⇒ the slope = 3

- In the equation y = -1/3 x + 4/3 ⇒ the slope = -1/3

* Now lets substitute the solution (-2 , 2) in the both equations

- First equation

∵ y = 2 ⇒ L.H.S

∵ 3(-2) + 8 = 2 ⇒ R.H.S

∵ L.H.S = R.H.S

∴ (-2 , 2) is a solution of the equation y = 3x + 8

- Second equation

∵ y = 2 ⇒ L.H.S

∵ (-1/3)(-2) + 4/3 = 2/3 + 4/3 = 6/3 = 2 ⇒ R.H.S

∵ L.H.S = R.H.S

∴ (-2 , 2) is a solution of the equation y = -1/3 x + 4/3

∴ (-2 , 2) is the solution of the two equations

* Its true

x = 3 ± √(5+y)