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4x + 3y = 8x + y so 3y - y = 8x - 4x ie 2y = 4x so y = 2x
4x + 3y = 1y = 2x + 8 Take the first part: 4x + 3y = 1y 4x = 1y - 3y 4x = -2y x = -y/2 Substitute x in second part: 1y = 2x + 8 1y = -2y/2 + 8 1y = -1y + 8 2y = 8 y = 4 Substitute y into either part: 1y = 2x + 8 1(4) = 2x + 8 4 - 8 = 2x -4 = 2x x = -2 Therefore: x = -2 y = 4
10x - 5y + 2x - 3y = 12x - 8y
5y-2y= 3y+2 5y-2y-3y= 2 0y= 2
2x+3y=12 ......1st equation 3x+2y=13 .......2nd equation ____________________________________ multiplying 1stt equation by 3 and 2nd equation by 2 3x(2x+3y=12) 2x(3x+2y=13) _______________________________ now the equations become 6x+9y=36 ...3rd 6x+4y=26 ....4th by solving both equation(substractinf 4th from 3rd) we get.. 5y=10 therefore y=2 and x=3
x=10 y=4
For y - 2y - 3y equals 0, y equals 0.
y=16 x= -4
2x - 3y = 2 3x + 2y = 3 Simultaneous Equations. Arbitrarily decide which letter to eliminate. In this case 'y'. To do this we bring the coefficients of 'y' to the same value. . To do this multiply the top equation by '2' and the bottom eq'n by.3. Hence 4x - 6y = 4 9x + 6y = 9 We now add the two equations. The addition of '-6y + 6y = 0 ', So 'y' is eliminated. Hence 13x = 13 x = 1 To find 'y' , we substitute 'x = 1' into either equation. Hence 4(1) - 6y = 4 4 - 6y = 4 -6y = 0 y = 0 So the answer in ( x,y ) form is ( 1,0 ) .
6x+7y=-6 3(-2x-3y=2) +________ -2y=0 => y=0 Therefore x=-1
2x - 3y = 4This can't be solved, although you can express each variable in terms of the other.x = (4-3y)/2y = (2x-4)/3
4x + 3y = 8x + y so 3y - y = 8x - 4x ie 2y = 4x so y = 2x
5x-2y+3z-2x-y-4z=3x-3y-z
2x-3y=5 and x-2y=12x-3y+2y=5 and x-2y+2y=12x-y=5 and x=12(1)-y=52-y=52-y-2=5-2-y=3y=-3(x,y) is (1,-3)
Multiply first equation by 1.5, giving 3x + 3y = 12, but we are told that 3x + 3y = 6. If there isn't an error in the question then 2 = 1!
2. If x=5 & y =3 then: 3x + 2y = 3 x 5 + 2 x 3 = 15 + 6 = 21 2x + 3y = 2 x 5 + 3 x 3 = 10 + 9 = 19 ⇒ 3x+2y exceeds 2x+3y by 21 - 19 = 2. Alternatively: 3x+2y exceeds 2x+3y by: (3x+2y) - (2x + 3y) = 3x + 2y - 2x - 3y = x - y If x=5 & y=3 then this becomes: x - y = 5 - 3 = 2
(-1, 0)