87.4k views
0 votes
Consider the system of linear equations:

kx+2y = 1
x+y = 1
​ Find all the value(s) of k for which the system of linear equations has a unique solution.
A. All k = 2
B. No value of k.
C. All values of k
D. Only k=2
E. Only k=1

User Krlos
by
8.0k points

1 Answer

4 votes

Final answer:

For the system of linear equations kx + 2y = 1 and x + y = 1 to have a unique solution, the value of k must be any number except 2. This is because the two lines must have different slopes to intersect exactly once.

Step-by-step explanation:

To find the value(s) of k for which the system of linear equations kx + 2y = 1 and x + y = 1 has a unique solution, we need to consider the coefficients. For a unique solution to exist in a system of two linear equations, the lines represented by these equations must intersect exactly once. This means that their slopes must be different. The slope-intercept form of a line is y = mx + b, where m is the slope.

The second equation is already in slope-intercept form, with a slope of -1. To find the slope of the first equation, we can rearrange it to solve for y: y = (1/2) - (k/2)x. The slope here is -k/2. These two slopes must be different for the equations to have a unique solution, so we set -k/2 not equal to -1 and solve for k:

-k/2 ≠ -1

Multiplying both sides by 2:

k ≠ 2

The system of equations will have a unique solution for all values of k except when k is 2. Therefore, the correct answer is All k ≠ 2 (All k not equal to 2).

User Rahul Ravi
by
8.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories