# Thread: Find solutions such that A: no solution, B: Unique solution C: Infinitely many

1. ## Find solutions such that A: no solution, B: Unique solution C: Infinitely many

Find solutions such that A: no solution, B: Unique solution C: Infinitely many

Question Details:

X1 + hX2 = 2
4X1+8X2= k

I get that h = -15 will be inconsistent (no solution)
h = Real number expect -15 will be unique ( i think)
I don't know how i will get infinitely many.

2. Originally Posted by nomana123
Find solutions such that A: no solution, B: Unique solution C: Infinitely many

Question Details:

X1 + hX2 = 2
4X1+8X2= k

I get that h = -15 will be inconsistent (no solution)
h = Real number expect -15 will be unique ( i think)
I don't know how i will get infinitely many.
I'm assuming the X1 and X2 are subscripted.

$x_1 + hx_2 = 2$

$4x_1 + 8x_2 = k$

no solution if $h = 2$ and $k \ne 8$

unique solution if $h \ne 2$

infinite solutions if $h = 2$ and $k = 8$

3. ## only unique answers for this

I wanted to ask this question original sorry. Thank you.

1 -3 -2
5 h -7

If, -5R1 + R2
= 1 -3 -2
0 15+h 3

now when h = -15 => inconsistent, when h doesn't equal -15 unique solutions. Infinite is not possible?