2x+5y+4z=0 Formula ①

3x+y-7z=0 Formula ②

x+y-z=？ Formula ③

Formula ①=0 and Formula ②=0, so Formula ①-Formula ③ = Formula ②-Formula ③.

Namely: 2x+5y+4z-x-y+z = 3x+y-7z-x-y+z.

x+4y+5z=2x+0y-6z

Exchange: x=4y+ 1 1z formula ④

From Formula ①: 2x=-5y-4z Formula ⑤

From Formula ②: 3x=-y+7z Formula ⑥

Formula ④×6: 6x=24y+66z Formula ⑦

Formula ⑤×3: 6x=-30y-24z Formula ⑧

Formula ⑥×2: 6x=-2y+ 14z Formula ⑨

Formula ⑦ Formula ⑧ Formula ⑨ constitutes an equation.

Solution: 54y+42z=0 -32y- 10z=0.

Approximate score: 9y+7z=0-16y-5z=0.

Multiplication: 45y+35z = 0-112y-35z = 0.

Solution: 45y- 1 12y=0.

So: y=0

Substitute the above formula layer by layer to get z=0 and x=0.

Therefore, x+y-z=0.

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Solution 2:

2x+5y+4z=0 Formula ①

3x+y-7z=0 Formula ②

x+y-z=？

Formula ①×3- Formula ②×2

3(2x+5y+4z)-2(3x+y-7z)=0

15y+ 12z-2y+ 14z = 0

13y+26z=0 Formula ③

Formula ①-Formula ②×5

(2x+5y+4z)-5(3x+y-7z)=0

-13x+39z=0 Type ④

Derived from formula ③

y=-2z

Derived from formula ④

x=3z

Substitute Formula ③ and Formula ④ into the original formula.

So:

x+y-z=3z+(-2z)-z=0

So the answer is: 0.