Question

solve the following linear equation by substitution:
5x-y=-6
-5x-4y=-24

Answer 1

consistent, inconsistent, or dependent?

Answer 2

this is a pair of consistent equations

we can put them in the form
5x-y +6 = 0
-5x-4y+24 = 0

now we take ratios of coefficients of similar terms where a1 and a2 are coefficients of x, b1 and b2 are coefficients of y and c1 and c2 are the constants

if a1/a2 not equal to b1/b2 then they are consistent and hv unique solutiion
if a1/a2 = b1/b2 = c1/c2 then they are consistent and hv infinite solutions and hence are dependent
if a1/a2 = b1/b2 not equal to c1/c2 then they are inconsistent

In above case 5/-5 is not equal to -1/-4 so they are consistent and have a unique solution

Hope this clears it for u.....