x + y = -1 (a) 4x - 3y = 12 (b) 3(a)+(b) gives 3x + 3y + 4x - 3y = -3 + 12 or 7x = 9 or x = 9/7 then x + y = -1 gives y = -1 -x = -1 - 9/7 = -16/7 So, x = 9/7 and y = -16/7
12-3y = 15 -3y = 15-12 -3y = 3 y = -1
4x+3y = 12 3y = -4x+12 y = -4/3x+4
-8x+3y=12 3y = 8x+12 y = (8/3)x + 4 So it will be a line with slope 8/3 and y intercept of 4
(3y2 - 3y)/(y - 1) = 3y(y - 1)/(y - 1) = 3y
3x 3y + 6z = 12
post an equation first.
3y+2z
x + y = -1 (a) 4x - 3y = 12 (b) 3(a)+(b) gives 3x + 3y + 4x - 3y = -3 + 12 or 7x = 9 or x = 9/7 then x + y = -1 gives y = -1 -x = -1 - 9/7 = -16/7 So, x = 9/7 and y = -16/7
12+3(y) 12+ 3(-3) 12 + {3x (-3)} 12+ (-9) 12-9 3
9
-9
3x + y + z = 63x - y + 2z = 9y + z = 3y + z = 3y = 3 - z (substitute 3 - z for y into the first equation of the system)3x + y + z = 63x + (3 - z) + z = 63x + 3 = 63x = 3x = 1 (substitute 3 - z for y and 1 for x into the second equation of the system)3x - y + 2z = 93(1) - (3 - z) + 2z = 93 - 3 + z + 2z = 93z = 9z = 3 (which yields y = 0)y = 3 - z = 3 - 3 = 0So that solution of the system of the equations is x = 1, y = 0, and z = 3.
Mid-point: (3z+z)/2, (2z+8z)/2 = (2z, 5z) Slope: (8z-2z)/(3z-z) = 6z/2z = 3 Perpendicular slope: -1/3 Equation: y -5z = -1/3(x -2z) => y = -1/3x+2z/3+5z => y = -1/3x+17z/3 General form of the bisector equation: x+3y-17z = 0
Rearrange the equations in the form of: x+3y = 17z 3*(3x-y = z) Multply the second equation by 3: x+3y = 17z 9x-3y = 3z Add them together to eliminate y: 10x = 20z Divide both sides by 10: x = 2z Substitute the value of x into the original equations to find the value of y: Therefore the point of intersection is: (2z, 5z)
12-3y = 15 -3y = 15-12 -3y = 3 y = -1
5y = 3y + 12 5y - 3y = (3y - 3y) + 12 2y = 12 y = 6