Question

On comparing the ratios a1 upon a2,b1 upon b2 and C1 upon c2
find out whether the following pair of
linear equations are consistent or inconsistent
2x+y =6 ,4x - 2y = 4​

Answer 1

(i) 3x + 2y = 5 ; 2x - 3y = 7 a1/a2=3/2 b1/b2=-2/3 and c1/c2=5/7 Hence, a1/a2 ne b1/b2 These linear equations are intersecting each other at one point and thus have possible solution. only one Hence, the pair of linear equations is consistent. (ii) 2x - 3y = 8 ; 4x - 6y = 9 a1/a2=2/4=1/2 b1/b2=-3/-6=1/2 and c1/c2=8/9 Hence, a1/a2=b1/b2 ne c1/c^ Therefore, these linear equations are parallel to each other and thus have no possible solution. Hence, the pair of inconsistent. linear equations is (iii) 3/2 * x + 5/3 * y = 7 ; 9x - 10y = 14 a1/a2=3/2/9=1/6 b1/b2=5/3/-10=-1/6 and C1/c2=7/14=1/2 Hence, a1/a2 ne b1/b2 Therefore, these linear equations are intersecting each other at one have only one possible pair of linear equations is consistent. point and thus solution. Hence, the ( iv) 5x-3y=11;-10x+6y=-22 a1la2 - 51-10 - -1/Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions. Hence, the pair of linear equations is consistent. (v) 4/3 * x + 2y = 8 ; 2x + 3y = 12 11/a2=4/3/2=2/3 b1/b2=/3 and 1/c2=8/12=2/3 Hence, a1/a2=b1/b2=c1/c2 Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions. Hence, the pair of linear equations is consistent.