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?

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.

Explanation:

The solution is where the lines intersect which is at the point (3,2).

So the answer is Option D.

The point (3,2) satisfies both equations.

Answer 2

Answer: The correct option is

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

Step-by-step explanation: Given that the two lines A and B are represented by the following equations :

Line A: y = x − 1

Line B: y = −3x + 11

We are to select the correct option that shows the solution to the above system of equations with reason.

The solution to the above system of linear equations will be the point through which both the lines A and B passes.

Now, comparing the values of y from both the equations, we get

`x-1=-3x+11\\\\\Rightarrow x+3x=11+1\\\\\Rightarrow 4x=12\\\\\Rightarrow x=(12)/(4)\\\\\Rightarrow x=3.`

And, from first equation, we get

`y=x-1=3-1=2.`

Thus, the required solution is (3, 2) because both the lines pass through this point.

Option (D) is CORRECT.