Question

Two lines, A and B, are represented by the equations given below:

Line A: y = x − 6
Line B: y = 3x + 4

Which of the following shows the solution to the system of equations and explains why?

(−5, −11), because the point satisfies both equations
(−5, −11), because the point does not lie on any axis
(−3, −5), because the point satisfies one of the equations
(−3, −5), because the point lies between the two axes

Answer 1

(−5, −11), because the point satisfies both equations

Explanation:

A solution to a system is always the ordered pair that satisfies both equations. So this explanation is the only one that would make sense.

Answer 2

Answer: (−5, −11), because the point satisfies both equations

Explanation:

The given system of equations of line A and B is :

Line A:
`y = x- 6`

Line B:
`y = 3x + 4`

To find the solution of the above system, we need to find the intersection point such that the point satisfies both equations.

Using elimination method, eliminate equation of Line A from equation of Line B, we get

`0=2x+10\\\\\Rightarrow\ 2x=-10\\\\\Rightarrow\ x=-5`

Put x = -5 in equation of Line A , we get

`y=-5-6=-11`

Hence, the solution to the system of equations is (-5,-11) because the point satisfies both equations.