3x+4z=-9, 2y-z=-5, 5x+3y=-7?

2008-06-28 6:19 pm
Solve by elimination method.

3x+4z=-9
2y-z=-5
5x+3y=-7

回答 (7)

2008-06-28 6:34 pm
✔ 最佳答案
x=1
y=-4
z=-3

3x+4z= -9 ---- eqn 1
2y-z= -5 ----- eqn 2
5x+3y= -7 ----- eqn 3

add eqn 1,eqn 2,eqn 3

8x+5y+3z= -21 ---- eqn 4

solving
eqn 4 ---- 8x+5y+3z= -21
eqn 2 X 3 --- 6y-3z= -15
8x+11y= -36 -------- eqn 5

solving
eqn 5 X 3 ----- 24x+33y= -108
eqn 3 X 11----- 55x+33y= -77
-31x= -31
x=1

substitute x=1 in eqn 3
5(1)+3y= -7
5+3y= -7
3y= -12
y= -4

substitute y= -4 in eqn 2
2(-4)-z=-5
-8-z= -5
-z= 3
z= -3
2016-10-13 7:41 pm
2 - (4z - 5) = 8 => 2 - 4z + 5 = 8 => - 4z = 8 - 7 => z = -(a million/4) = - 0.25 (2x + 3) - (5x - 7) = a million => 2x + 3 - 5x + 7 = a million => -3x = a million - 10 => -3x = -9 => x = 3 3 (n - 2) - 2 (3 - n) = 4(n - 3) => 3n - 6 - 6 + 2n = 4n - 12 => 5n - 12 = 4n - 12 => 5n - 4n = -12 + 12 => n = 0 3(4u - 6) = 2(4u - 3) - (u - 8) => 12u - 18 = 8u - 6 - u + 8 => 12u - 18 = 7u + 2 => 12u - 7u = 2 + 18 => 5u = 20 => u = (20/5) = 4 y(2 - 4) = 6 - (y2 + 3y - y) => 2y - 4y = 6 - (y2 + 2y) => -2y = 6 - (4y) => 2y = 6 => y = 3
2008-06-28 6:57 pm
3x + 4z = - 9
8y - 4z = - 20------ADD

3x + 8y = - 29
5x + 3y = - 7

- 15x - 40y = 145
15x + 9y = - 21---------ADD

- 31y = 124
y = - 4

3x - 32 = - 29
3x = 3
x = 1

3 + 4z = - 9
4z = - 12
z = - 3

x = 1 , y = - 4 , z = - 3
2008-06-28 6:37 pm
3x + 4z = -9
2y - z = -5
5x + 3y = -7

3x + 4z = -9
3x + 0y + 4z = -9
5(3x + 0y + 4z) = 5(-9)
15x + 0y + 20z = -45

5x + 3y = -7
5x + 3y + 0z = -7
3(5x + 3y + 0z) = 3(-7)
15x + 9y + 0z = -21

...15x + 0y + 20z = -45
-- 15x + 9y + 0z = -21 (subtraction)
----------------------------------
-9y + 20z = -24

-9y + 20z = -24
2(-9y + 20z) = 2(-24)
-18y + 40z = -48

2y - z = -5
-9(2y - z) = -9(-5)
-18y + 9z = 45

...-18y + 40z = -48
-- -18y + 9z = 45
-----------------------------
31z = -93

31z = -93
z = -93/31
z = -3

3x + 4z = -9
3x + 4(-3) = -9
3x - 12 = -9
3x = -9 + 12
3x = 3
x = 3/3
x = 1

5x + 3y = -7
5(1) + 3y = -7
5 + 3y = -7
3y = -7 - 5
3y = -12
y = -12/3
y = -4

∴ x = 1 , y = -4 , z = -3
2008-06-28 6:35 pm
3x+4z=-9----- (1)
2y-z=-5 --------(2)
5x+3y=-7 ------(3)
From (2)
-z=-5-2y
z=5+2y -------(4)

putting (4) in (1)
3x+4(5+2y)=-9
3x+20+8y=-9
3x+8y=-9-20
3x+8y=-29
3x=-29-8y
x=-(29+8y)/3 -------- (5)

Putting (5) in (3)
5x+3{-(29+8y)/3}=-7
5x-29-8x=-7
3x=-7+29
3x=22
x=22/3
putting x=22/3 in (5)
22/3=-(29+8y)/3
22=-29-8y
8y=-29-22
8y=-51
y=-51/8

putting y=-51/8 in (4)
z=5+2(-51/8)
z=5-52/4
z=(20-51)/4
z=-31/4

Hence, x=22/3, y=-51/8 and z=-31/4
2008-06-28 6:34 pm
x=1 y=-4 z=-3
2008-06-28 6:30 pm
8x +3z + 5y that is sort ov wot it wud be if it did not av the answer already so i ave no idea


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