Sunday

November 23, 2014

November 23, 2014

Posted by **Dan** on Tuesday, December 18, 2012 at 2:42pm.

x-2y=k-1

4x+(1-k^2)y=8

For what values of k does the system have

a. unique solution?

b. infinitely many solutions?

c. no solution?

- Linear Algebra -
**Steve**, Tuesday, December 18, 2012 at 2:59pmrearranging things a bit, you have

y = x/2 + (1-k)/2

y = 4x/(k^2-1) + 8/(1-k^2)

for infinitely many solution, we need

y = mx+b

y = mx+c

where b=c

same slope:

1/2 = 4/(k^2-1)

k^2-1 = 8

k^2 = 9

k = ±3

b=c:

(1-k)/2 = 8/(1-k^2)

(1-k)(1-k^2) = 16

k=3

So, if k=3 there are infinitely many solutions.

If k = -3, there are no solutions.

For any other value of k, there is one solution.

- Linear Algebra -
**Dan**, Tuesday, December 18, 2012 at 5:40pmCan you perform using matrix? Thank you very much

**Answer this Question**

**Related Questions**

Linear algebra - Consider for every real number a the linear system of equations...

Algebra - Suppose a linear system of equations has 2012 equations and 2013 ...

math - A linear system may have a unique solution, no solution, or infinitely ...

math - A linear system may have a unique solution, no solution, or infinitely ...

MAT222 - -x+2y=-2 x-2y=2 the system has no solution the system has a unique ...

math - two systems of equations are giving below for each system choosethe best ...

Linear Algebra - For which values of 'a' will the following system have no ...

Grade 10 Math - Write an equation that forms a system of equations with x + y = ...

Algebra 2 Helpp :( - QUESTIONS (vvv) (1) Solve the system by subsitution 2x + y...

MAT222 - -x+4y=4 x-4y=-4 the system has no solution the system has a unique ...