Q.1). Solve for x and y? 1)6(ax+by)=3a+2b 6(bx-ay) =3b-2a

1.	Q.1). Solve for x and y? 1)6(ax+by)=3a+2b 6(bx-ay) =3b-2a
Answer» 6(ax + by) = 3a + 2b6ax + 6by = 3a + 2b.........(i)6(bx - ay) = 3b - 2a6bx - 6ay = 3b - 2a.........(ii)Multiplying (i) by a and (2) by b,So, 6a2x + 6aby = 3a2 + 2ab .......... (iii)And 6b2x - 6aby = 3b2 - 2ab ......... (iv)Add (iii) and (iv), we get6a2x + 6aby + 6b2x - 6aby = 3a2 + 2ab + 3b2 - 2ab⇒ 6a2x + 6b2x = 3a2\xa0+ 3b2⇒6 (a2x + b2x) = 3(a2\xa0+ b2)⇒{tex}x = \\frac { 3 \\left( a ^ { 2 } + b ^ { 2 } \\right) } { 6 \\left( a ^ { 2 } + b ^ { 2 } \\right) } = \\frac { 3 } { 6 } = \\frac { 1 } { 2 }{/tex}Substituting\xa0{tex}x = \\frac 12{/tex}\xa0in (i),we get{tex}6 a \\times \\frac { 1 } { 2 } + 6 b y = 3 a + 2 b{/tex}⇒ 3a + 6by = 3a + 2b⇒ 6by =3a + 2b -3a⇒ 6by = 2b⇒ {tex}y = \\frac { 2 b } { 6 b } = \\frac { 1 } { 3 }{/tex}Hence, the solution is\xa0{tex}x = \\frac { 1 } { 2 } , y = \\frac { 1 } { 3 }{/tex}

Discussion