Question

Solve the following system:
x - y + z = 0
3x - 2y + 5z = 8
2x + y - 3z = -9

Answer 1

id suggest you pick 1 variable on the first line, maybe x, and rewrite it.

x = y - z. now plug this is for x in the 2nd and 3rd row. this will eliminate x completely.

you can then do the same concept as you did for x for either y or z in the 2nd row, to be done in the 3rd

Answer 2

Another possibility is to multiply the third equation by 2 and add it to the second to get an equation in x and z.

Then multiply the first equation by 2 and subtract it from the second to get another equation in x and z.

U now have simultaneous equations in x and z which you can solve normally.

Sub back to get y.

Answer 3

x - y + z = 0 ----------(1)
3x - 2y + 5z = 8 ----------(2)
2x + y - 3z = -9 ----------(3)

first use (1) and (2) to eliminate x
x - y + z = 0 ----------(1) multiply by -3
3x - 2y + 5z = 8 ----------(2)

-3x + 3y - 3z = 0
3x - 2y + 5z = 8 add these two to get
y + 2z = 8 ---------------(4)

now use (2) and (3) to eliminate x
3x - 2y + 5z = 8 ----------(2) multiply by 2
2x + y - 3z = -9 ----------(3) multiply by -3

6x - 4y + 10z = 16
-6x - 3y + 9z = 27 add these two to get
- 7y + 19z = 43 --------------(5)

Answer 4

more following...

Answer 5

now take (4) and (5) to eliminate y
y + 2z = 8 --------------(4) multiply by 7
-7y + 19z = 43 --------------(5)

7y + 14z = 56
-7y + 19z = 43 add these two to get
33z = 99
z = 99/33 = 3 so z = 3 <<<<<

substitute z = 3 in y + 2z = 8 --------------(4) to get

y + 2(3) = 8
y = 8 - 6
y = 2 so y = 2 <<<<<

substitute y = 2 and z = 3 in x - y + z = 0 ----------(1)

x -(2) + (3) = 0
x - 2 + 3 = 0
x + 1 = 0
x = -1 so x = -1 <<<<<


so solution is (x, y, z) = (-1, 2, 3)

Answer 6

i hope the method is clear .....☺