x = -4y so 3x = -12y Substituting in the second equation, -12y + 2y = 20 or -10y = 20 ie y = -2 And then x = -4y implies that x = 8 Solution: x = 8, y = -2
(2, -1)
Subtract: 3x - 3x - 4y - 2y = 30 - 6 ie -6y = 24 so y = -4 and x = 14/3
3x + 4y = 5x - 2y = 5leads to:x = 5 + 2ySo:3(5 + 2y) + 4y = 515 + 10y = 510y= -10y=-1and therefore if y = -1 then x = 3.
(-1, 5)
3x - 2y = 20 Substitute x = 4y into this equation: 3(4y) - 2y = 20 ie 12y - 2y = 20 10y = 20 so that y = 2 and then x = 4y gives x = 2*4 = 8
x = 4y 3x - 2y = 20 Substituting the value of x into the second equation, 3*(4y) - 2y = 20 ie 12y - 2y = 20 or 10y = 20 so that y = 2 Then x = 4y = 4*2 = 8. So (x , y) = (8 , 2)
x = -4y so 3x = -12y Substituting in the second equation, -12y + 2y = 20 or -10y = 20 ie y = -2 And then x = -4y implies that x = 8 Solution: x = 8, y = -2
(2, -1)
Subtract: 3x - 3x - 4y - 2y = 30 - 6 ie -6y = 24 so y = -4 and x = 14/3
3x - 4y = -1
4y = 2y + 40 4y - 2y = 2y -2y +40 2y = 40 y = 20 check 4(20) = 2(20) +40 80 = 80
3x - 2y + 7x + 4y = 3x + 7x - 2y +4y = (3+7)x + (-2+4)y = 10x + 2y
parallel
The equation can be simplified to show a value of Y in terms of X. 3X + 2Y +2 = 4Y + 4 3X + 2 = 2Y + 4 3X -2 = 2Y and 2Y = 3X - 2 means that Y = (3/2 X) -1
3x + 4y = 5x - 2y = 5leads to:x = 5 + 2ySo:3(5 + 2y) + 4y = 515 + 10y = 510y= -10y=-1and therefore if y = -1 then x = 3.
(-1, 5)