2X + 6Y = 12 3X + 9Y = 18 try elimination - 3(2X + 6Y = 12) 2(3X + 9Y = 18) - 6X - 18Y = - 36 6X + 18Y = 36 ================= I will say this system is dependent and an infinite number of solutions can be found.
y-3x+6y=12 7y=3x+12 y=3x/7 +12/7
3x + 6y + 6x = 9x + 6y which can be factorised as 3(3x +2y)
3x-6y=12; subtract 12 & add 6y to both sides 3x-12=6y; divide by 6 (1/2)x-2=y; re-write y=(1/2)x-2 slope intercept form
3x - 6y = 9, 5x + 4y = -27 6x - 12y = 18, 15x + 12y = -81 21x = -63 x = -3 (3 x -3) = 9 + 6y (-9 - 9)/6 = y y = -3 Check: (5 x -3) + (4 x -3) = -15 -12 = -27 QED
Let's see. Looks like easy substitution here. X - 2Y = 6 3X - 6Y = 18 express one variable in term of another with top equation X - 2Y = 6 X = 2Y + 6 insert into bottom equation 3(2Y + 6) - 6Y = 18 6Y + 18 - 6Y = 18 ---------------------------------admits of no solution here, try elimination - 3(X - 2Y = 6) 3X - 6Y = 18 - 3X + 6Y = - 18 3X - 6Y = 18 This system either admits of no solution, or an infinite number of solutions, but my systems work is rusty, so I do not remember the terms
3x-6y=9 -3x -3x -6y=9-3x __ ____ -6 -6 y=9-3x ____ -6
6y = 3x + 4
3x-6y=-8
3x + 6y = 363x - 6y = 0 add both equations6x = 36x = 63x - 6y = 03(6) - 6y = 018 - 6y = 018 = 6y3 = yThe solution point is (6, 3).
5x2y = 3x - 6y 5x2y + 6y = 3x y(5x2 + 6) = 3x y = (3x)/(5x2 + 6) This is a rational function.
2X + 6Y = 12 3X + 9Y = 18 try elimination - 3(2X + 6Y = 12) 2(3X + 9Y = 18) - 6X - 18Y = - 36 6X + 18Y = 36 ================= I will say this system is dependent and an infinite number of solutions can be found.
no
3x - 6y = 9Subtract 3x from each side:-6y = -3x + 9Multiply each side by -1 :6y = 3x - 9Divide each side by 6:y = 0.5x - 1.5
y = -1x/2 3x + 6y = 0 -3x -3x __________ 6y = 0 - 3x --- -------- 6 6 y= -3x/6 y= -1x/2
distribute property
y-3x+6y=12 7y=3x+12 y=3x/7 +12/7