State whether the system is consistent and independent, consistent and dependent, or inconsistent.?

Question

(1) 4x + 2y = 8
2x + y = 1

(2) x + y = 4
2x - y = -7

Answer 1

(1) 4x + 2y = 8 --> y= -2x +8
2x + y = 1--> y -2x +1
These lines have the same slope and different x-intercepts so they are parallel and incosistent.

(2) x + y = 4 --> y = -x +4
2x - y = -7 --> y = 2x +7
Thes two lines have different slopes and y-intercepts so they will intersect at just 1 point. Thus they are consitent and independent

Answer 2

(1) inconsistent
2x+y=1=4

(2)consistent and independent
x= -1, y=5

Answer 3

x = 2y - 3 We have already got x appropriate set up so we merely exchange x with cost 2y - 3 in 2nd equation: device is inconsistent whilst there are no longer any strategies (2 parallel strains) in any different case device is consistent. whilst platforms is consistent, we've 2 opportunities: device relies upon (infinite strategies, 2 equations of comparable line) device is autonomous (one answer ---> intersecting strains) So announcing platforms is consistent isn't adequate. we ought to appreciate notwithstanding if it relies upon or autonomous. ------------------------------ 2x - 3y = -5 2 (2y - 3) - 3y = -5 4y - 6 - 3y = -5 y = -5 + 6 y = a million x = 2y - 3 = 2 - 3 = -a million answer: (-a million, a million) platforms is autonomous ------------------------------- notice which you will consistently verify if device of two linear equations relies upon, autonomous, or inconsistent with no need to discover an exact answer. M?thm?m

Answer 4

I'll say, since system of equations (1) has no solution, they are inconsistent.

No. (2) has a solution, so they are consistent and dependent...