Question

Two lines, A and B, are represented by equations given below: Line A: y = x − 4 Line B: y = 3x + 4 Which of the following shows the solution to the system of equations and explains why? (1 point) a (−3, −5), because the point satisfies one of the equations b (−3, −5), because the point lies between the two axes c (−4, −8), because the point satisfies both equations d (−4, −8), because the point does not lie on any axis

Answer 1

The answer is "C"

Explanation:

Answer 2

Answer C. This point lies between the two axes and its coordinates satisfy both equations

Explanation:

Line A: y = x − 4

Line B: y = 3x + 4

Let's actually solve this system, using substitution: Equate

Line A: y = x − 4 to Line B: y = 3x + 4, obtaining:

x − 4 = 3x + 4

Subtract (x - 4) from both sides. Doing so yields

0 = 2x + 8, and so x = -4.

From Line A let's find y: Letting x = -4, we get: y = -4 - 4 = -8

and so the solution is (-4, -8). This matches Answer C. This point lies between the two axes and its coordinates satisfy both equations.