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Solve this system of equations. 5x+3y+z=-29 x-3y+2z=23 14x-2y+3z=-18 Write the solution as an ordered triple.
if you have one equation that gives you x or y use substitution x+3y=18 x= 18-3y substitute (18-3y) for x in the other equation if you have coefficients that will not 'reduce' use elimination 2x+3y= -3 5x-4y=9 watch for equations that will reduce 2x+4y= -8 divide through by 2 x+2y= -4 x= -4-2y
3y + 4z + 12y = 3y -3y -3y ------------------------- 4z + 12y = 0 divide everything by 4 z + 3y = 0 -3y -3y z = -3y
you begin with -7x+y=-20 and 9x-3y=36 7x-7x+y=-20+7x (add 7x to both sides) y=7x-20 (simplify) 9x-9x-3y=36-9x (subtract 9x from both sides) -3y/-3=36/-3-9x/-3 (divide both sides by -3) y=3x-12 (simplify) y=y so 7x-20=3x-12 7x+20-20=3x-12+20 (add 20 to both sides) 7x=3x+8 (simplify) 7x-3x=3x-3x+8 (add 3x to both sides) 4x=8 (simplify) 4x/4=8/4 (divide by 4 on both sides) x=2 (simplify) 9(2)-3y=36 (plug in 2 for x) 18-3y=36 (simplify) 18-18-3y=36-18 (subtract 18 from both sides) -3y=18 (simplify) -3y/-3=18/-3 (divide by -3 on both sides) y=-6 (simplify) the point is 2,-6 (x,y)
-2x+3y=-18
5y - 3y = 18 2y = 18 y = 18/2 y = 9
21
-2 = 3y-18-5y 16=3y-5y 16=-2y y=-8
9y - 18 = 3y subtract 3y from both sides 6y - 18 = 0 add 18 to both sides 6y = 18 divide by 6 on both sides y = 3
given is that 4x+3y=6(3x+3y)=7 i.e., 6(3x+3y)=7 &&& 4x+3y=7 ---------------(1) 3x+3y=7/6 x+y=7/18 _________(2) multiply eqn(2) by 4 4x+4y=28/18 -------------------------(3) (3)-(1) 4x+3y-4x-4y=7-(28/18) y= -98/18 substitute y in eqn(2) x-98/18=7/18 x=7/18+98/18 x=105/18. therefore x=105/18 : y= -98/18
6x+3y = 18 3y = -6x+18 y = -2x+6 Therefore the slope is -2 and the y intercept is 6
9x + 3y = -54 3y = -9x - 54 y = -(3x + 18) Therefore, the y-intercept of this equation is y=-18.
2x + 3y = 18 2x - 3y = 20
This is not an equation because there's no equal sign If you mean: 6x -3y = 18 Then -3y = -6x+18 And: y = 2x-6 So the slope is 2 and the y intercept is -6
3y + 18 = -8x + 3Subtract 18 from each side:3y = -8x - 15Divide each side by 3:y = (-8/3)x - 5
Convert the equation into the form y = mx + c, where m is the slope (and c is the y intercept) 2x + 3y = 18 3y = -2x + 18 y = -2/3x + 6 Therefore the slope is -2/3.