Question

Solve the following system of equations for all three variables.

-2x + 3y – 4z = 8
5x – 3y + 5z = -8
7x – 3y + 3z = 8
X =
1
y =
2
Z =
3
Submit Answer

Answer 1

Answer: Given equations

2x+3y−z=6 →(1)

x−y+7z=8 →(2)

3x−y+2z=7 →(3)

(1)+3×(2)

2x+3y−z+3x−3y+21z=6+24

5x+20z=30

x+4z=6 →(4)

(3)−(2)

2x−5z=−1 →(5)

2×(4)−(5)

2x+8z−2x+5z=12=1

13z=13

z=1

x=6−4z

x=2

⇒ 2(2)+3y−1=6

y=1

∴ x=2,y=1,z=1 is solution of given equations.

Step-by-step explanation: hope it is help full

Answer 2

Explanation:

-2x + 3y – 4z = 8 ----------------(I)

5x – 3y + 5z = -8 -----------------(II)

7x – 3y + 3z = 8 ------------------(III)

Add equation (I) & (II) and thus y will be eliminated

(I) -2x + 3y – 4z = 8

(II) 5x – 3y + 5z = -8 {Add}

3x + z = 0 ------------------------(A)

Multiply equation (II) by (-1) and then add with equation (III). Thus y will be eliminated.

(II) * (-1) -5x + 3y - 5z = +8

7x – 3y + 3z = 8 {Add}

2x -2z = 16 ---------------(B)

Multiply equation (A) by 2 and then add. Thus z will be eliminated and we will get the value of x

(A) * 2 6x + 2z = 0

(B) 2x - 2z = 16 {Add}

8x = 16

Divide both sides by 8

x = 16/8

x = 2

Plugin x = 2 in equation (A)

3x + z = 0

3*2 + z = 0

6 + z = 0

z = -6

Plug in x = 2 and z = - 6 in equation (I)

-2x +3y - 4z = 8

-2*2 + 3y - 4*(-6) = 8

-4 + 3y + 24 = 8

3y + 20 = 8

3y = 8 - 20

3y = -12

y = -12/3

y = -4