Explanation
The given equations are⇒16x+3+3y−2=5....eq(1)⇒16x+3+3y−2=5....eq(1)⇒8x+3−1y−2=0....eq(2)⇒8x+3−1y−2=0....eq(2)Put1x+3=u and 1y−2=v in eq(1)and(2)Put1x+3=u and 1y−2=v in eq(1)and(2)⇒16u+3v=5....eq(3)⇒16u+3v=5....eq(3)⇒8u−v=0....eq(4)⇒8u−v=0....eq(4)multiply eq(4) by 3 and subtract eq(3)and eq(4)multiply eq(4) by 3 and subtract eq(3)and eq(4)⇒(16u+3v=5)−(24u−v=0)⇒(16u+3v=5)−(24u−v=0)⇒40u=5⇒u=18⇒40u=5⇒u=18Putu=18 in eq(3)Putu=18 in eq(3)⇒16(18)+3v=5⇒3v=3⇒v=1⇒16(18)+3v=5⇒3v=3⇒v=1Hence,1x+3=u=18⇒x+3=8⇒x=5Hence,1x+3=u=18⇒x+3=8⇒x=51y−2=v=1⇒y−2=1⇒y=31y−2=v=1⇒y−2=1⇒y=3
The given equations are⇒242x+y−133x+2y=2...eq(1)⇒242x+y−133x+2y=2...eq(1)⇒263x+2y+82x+y=3...eq(1)⇒263x+2y+82x+y=3...eq(1)Put12x+y=u and 13x+y=v in eq(1)and(2)Put12x+y=u and 13x+y=v in eq(1)and(2)⇒24u−13v=2.....(3)⇒24u−13v=2.....(3)⇒8u+26v=3......(4)⇒8u+26v=3......(4)Multiply eq(3) by 26 and eq(4) by 13 and subtract bothMultiply eq(3) by 26 and eq(4) by 13 and subtract both⇒(624u−338v=52)−(104u+338v=39)⇒(624u−338v=52)−(104u+338v=39)⇒728u=91⇒u=18⇒728u=91⇒u=18Putu=18 in eq(4)Putu=18 in eq(4)⇒8×18+26v=3⇒26v=2⇒v=113⇒8×18+26v=3⇒26v=2⇒v=113Hence,u=12x+y=18⇒2x+y=8.....eq(5)Hence,u=12x+y=18⇒2x+y=8.....eq(5)v=13x+2y=113⇒3x+2y=13...eq(6)v=13x+2y=113⇒3x+2y=13...eq(6)Multiply eq(5) by 2 and subtract from eq(6)Multiply eq(5) by 2 and subtract from eq(6)⇒(4x+2y=16)−(3x+3y=13)⇒(4x+2y=16)−(3x+3y=13)⇒x=3⇒x=3put x=3 in eq(5)put x=3 in eq(5)⇒2×3+y=8⇒y=2⇒2×3+y=8⇒y=2
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