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Eiicanlenictieh ioe. ax +by+c=0, , in two variables {a#0,b#0&a,b,ce R}, ax+by+c¢,=0 .(1) e s F 3, 5 h 1 qv Solution (x,y) — point lying on, , , , , , , , , Substitution method ax+by+c,=0 .(2) i ;, ax+bytc,=0 zai) : ai i VVY Stott at y=2x-4, ax + b,y+ c, =0 (ii) v ( Equation of a \, , i) x= eb Methods to solve) ee, From eq, (i) x= : AAA, , , , , Substitute x in eq. (ii) and solve., = Dia — bot y= 2201-82 |, aide ~ aaby Stan e2i, , Elimination method, ax +byt+c,=0, , , , wee, {, Al method Graphical method, , Cross multiplication method, , , , , , , , , , , , , , , , Condition of Solvability of System of Linear Equations, , , , , ax +by+c,=0 z yi 5 re arn, i: 4 : ‘, , Multiply b, in (i) & b, in (ii) b. 7t Q, le b, Intereectng) > = # te, Unique solution, a,b,x+ bib.y + ¢, b, = 0 (iii) b =, oe 2p 4 (intersect at 1 point) (consistent), , . a c a; ie 4, b.a,x + bby + cb, = 0 iv) - ; ” ‘ | Coincident <<>> ae =e ea — Infinite solution, (3) -(4)..... . ERS UIG RS=aGh aDE=aDT | (Coincide) (consistent), (a,b,-b,a,)x + (c,b,-c,b,) = 0, , aa I Parallel S21 = 51 421 5 No solution, x = Diabet ye omar x= Pica book y= 2201-8102, i (No intersection) 82. be, 2 (inconsistent), Ayby — nb, @ybo — ab, ayb2 ~ ab, a2 —agb,, , , , , , , , e.g. Six years hence a man's age will be em, three times the age of his son and Ek a, toapairoflinear, , three years ago he was nine times e.g. Solve the following system of linear, as old as his son. Find their present ages. equations graphically :x—y=1, 2x+y=8., Sol. Let man's present age be ‘x’ yrs, & son's present age be ‘y’ yrs., , According to problem, , , , Sol.(i) x-y=1 0 1 2, , ery tA We -1|o] 1, , , , , , , , ii) 2x+y=8 T, oe x 0 1 2, y a] 6] 4, , x+6=3(y +6), , = 12... (i), , , , , , , , , , , , , , , , On solving equation (i) & (ii seosith, Peabo y =e. OS a) Solution is x = 3 and y=2, So, the present age of man = 30 years, and present age of son = 6 years., , , , , , NCERT / X/ Linear equation in two variable