Question

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

Line A: y = x − 1
Line B: y = −3x + 11

Which of the following options shows the solution to the system of equations and explains why? (4 points)

a
(3, 2), because the point does not lie on any axis

b
(3, 2), because one of the lines passes through this point

c
(3, 2), because the point lies between the two axes

d
(3, 2), because both lines pass through this point

Answer 1

d is correct

Explanation:

:)

Answer 2

The solution to the system of equations is (3, 2) and because both lines pass through this point.

Hence, option D is correct.

Explanation:

Given the system of equations

Line A: y = x − 1

Line B: y = −3x + 11

Arrange equation variables for elimination

`\begin{bmatrix}y-x=-1\\ y+3x=11\end{bmatrix}`

subtracting the equations

`y+3x=11`

`-`

`\underline{y-x=-1}`

`4x=12`

solving 4x = 12 for x

`4x = 12`

divide both sides by 4

`(4x)/(4)=(12)/(4)`

Simplify

`x = 3`

For y = x − 1, substutute x = 3

y = x-1

y = 3 - 1

y = 2

Thus,

(x, y) = (3, 2)

Therefore,

The solution to the system of equations is (3, 2) and because both lines pass through this point.

Hence, option D is correct.