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solve by elimination or substitution method
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solve by elimination or substitution method
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6x + 6y = 3 ------ × 4
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6By elimination method ....,
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6By elimination method ...., 24x + 24y = 12
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6By elimination method ...., 24x + 24y = 12 24x + 24y = 12 ( subtraction )
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6By elimination method ...., 24x + 24y = 12 24x + 24y = 12 ( subtraction ) ________________
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6By elimination method ...., 24x + 24y = 12 24x + 24y = 12 ( subtraction ) ________________ 0 = 0
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6By elimination method ...., 24x + 24y = 12 24x + 24y = 12 ( subtraction ) ________________ 0 = 0Since , LHS = RHS this given equation has infinitely many solutions and do not have a common solution
___________₹__₹₹_______________
-5x + 7y = 10 —--------- × 3
-5x + 7y = 10 —--------- × 315x - 21y = 22
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method .....,
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method ....., -15x + 21y = 30 ( addition )
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method ....., -15x + 21y = 30 ( addition ) 15x - 21y = 22
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method ....., -15x + 21y = 30 ( addition ) 15x - 21y = 22________________
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method ....., -15x + 21y = 30 ( addition ) 15x - 21y = 22________________ 0 = 8
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method ....., -15x + 21y = 30 ( addition ) 15x - 21y = 22________________ 0 = 8Since, 0 = 8 which is false statement . Therefore, the given equation do not have a common solution .
3)
3) -2x + y = 13
3) -2x + y = 13 x - 4y = -31 ------- × 2
By elimination method ,
-2x + y = 13
-2x + y = 13 2x - 8y = -62 ( addition )
-2x + y = 13 2x - 8y = -62 ( addition ) ____________
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7Put y = 7 in ( x - 4y = -31 )
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7Put y = 7 in ( x - 4y = -31 )=> x - 4 × 7 = -31
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7Put y = 7 in ( x - 4y = -31 )=> x - 4 × 7 = -31=> x - 28 = - 31
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7Put y = 7 in ( x - 4y = -31 )=> x - 4 × 7 = -31=> x - 28 = - 31=> x = - 31 + 28
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7Put y = 7 in ( x - 4y = -31 )=> x - 4 × 7 = -31=> x - 28 = - 31=> x = - 31 + 28= > x = -3
6x + 6y = 3 ------ × 4
4x + 4y = 2 ------ × 6
By elimination method ....,
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6By elimination method ...., 24x += 12
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6By elimination method ...., 24x + 24y = 12 24x + 24y = 12 ( subtraction )
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6By elimination method ...., 24x + 24y = 12 24x + 24y = 12 ( subtraction ) ________________
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6By elimination method ...., 24x + 24y = 12 24x + 24y = 12 ( subtraction ) ________________ 0 = 0
6x + 6y = 3 ------ × 44x + 4y = 2 ------ × 6By elimination method ...., 24x + 24y = 12 24x + 24y = 12 ( subtraction ) ________________ 0 = 0Since , LHS = RHS this given equation has infinitely many solutions and do not have a common solution
___________₹__₹₹_______________
-5x + 7y = 10 —--------- × 3
-5x + 7y = 10 —--------- × 315x - 21y = 22
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method .....,
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method ....., -15x + 21y = 30 ( addition )
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method ....., -15x + 21y = 30 ( addition ) 15x - 21y = 22
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method ....., -15x + 21y = 30 ( addition ) 15x - 21y = 22________________
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method ....., -15x + 21y = 30 ( addition ) 15x - 21y = 22________________ 0 = 8
-5x + 7y = 10 —--------- × 315x - 21y = 22By elimination method ....., -15x + 21y = 30 ( addition ) 15x - 21y = 22________________ 0 = 8Since, 0 = 8 which is false statement . Therefore, the given equation do not have a common solution .
3)
3) -2x + y = 13
3) -2x + y = 13 x - 4y = -31 ------- × 2
By elimination method ,
-2x + y = 13
-2x + y = 13 2x - 8y = -62 ( addition )
-2x + y = 13 2x - 8y = -62 ( addition ) ____________
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7Put y = 7 in ( x - 4y = -31 )
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7Put y = 7 in ( x - 4y = -31 )=> x - 4 × 7 = -31
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7Put y = 7 in ( x - 4y = -31 )=> x - 4 × 7 = -31=> x - 28 = - 31
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7Put y = 7 in ( x - 4y = -31 )=> x - 4 × 7 = -31=> x - 28 = - 31=> x = - 31 + 28
-2x + y = 13 2x - 8y = -62 ( addition ) ____________ - 7y = - 49 y = 7Put y = 7 in ( x - 4y = -31 )=> x - 4 × 7 = -31=> x - 28 = - 31=> x = - 31 + 28= > x = -3