10x - 5y + 2x - 3y = 12x - 8y
10x+2x-3y-4y=12x-7y
5y-2y= 3y+2 5y-2y-3y= 2 0y= 2
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
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
10x - 5y + 2x - 3y = 12x - 8y
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)
12x-8y
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
5x-2y+3z-2x-y-4z=3x-3y-z
(-1, 0)
If 3y = 12, 2y = 8
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
2x + 5y = 16 -2x - 3y = -14 2y = 2 y = 1 / x = 5.5 (5.5,1) or (5 1/2,1)
10x - 3y + 2x - 4y =(10x + 2x) + (-3y - 4y) =12x - 7y
3y2 - 2y + 6xy - 4x = y(3y - 2) + 2x(3y - 2) = (y + 2x)*(3y - 2)
-4(7x-3y-z)-(-6)(9x-z+2)