Let z be known and solve the equations of x and y.

3x+7y+z=3. 15…… 1

4x+ 10y+z=4.20……2

1x 4: 12x+28y+4z = 3. 15x 4...3

2x3: 12x+30y+3z = 4.20x3 ...

4-3: 2y-z = 4.20x3-3. 15x4...a

and

1x 10:30x+70y+ 10z = 3. 15x 10...5

2x7: 28x+70y+7z = 4.20x7...6

5-6:2x+3z = 3. 15x 10-4.20 x7...b

a+b:2x+2y+2z = 4.20 x3-3. 15x 4+3. 15x 10-4.20 x7 = 3. 15x 6-4.20 x4 = 2. 1。

Then x+y+z= 1.05.

Second, clever way:

3x+7y+z=3. 15…… 1

4x+ 10y+z=4.20……2

1x 6: 18x+42y+6z = 3. 15x 6...3

2x4: 16x+40y+4z = 4.20x4 ...

3-4:2x+3y+2z = 3. 15x 6-4.20 x4 = 2. 1。

So:

Then x+y+z= 1.05.

Summary: Generally speaking, it is impossible to find the value of x+y+z for the two equations of x, y, z Y and z!

Since this problem requires the value of x+y+z, it shows that the coefficients of the two equations just meet this special case. You can study its characteristics carefully, but it is of little significance to solve mathematical problems.

"Basic method" is the most useful! Solve the equations of x, y: finally calculate x+y+z, and z should be eliminated. If z cannot be eliminated, it means that x+y+z has no definite value!

The "ingenious method" needs to be observed and difficult to master. It is better to use the "basic method" to calculate. I also calculated it with the basic method first, and finally found its law when 2x+2y+2z=3. 15x6-4.20x4, and then summed up the "ingenious method".