Solve the system of equations. 2x+2y+3z=3 6x+3y+3z=3 2x+5y=6z=6

x = -1/5 , y = 4/5 , z = 3/5

Step-by-step explanation:

Pls note a typo in your question 2x+5y=6z=6, I changed it to 2x+5y=6z, in any case if you didn't make a typo there is no solution.

Solve the following system:

{2 x + 2 y + 3 z = 3 | (equation 1)

{6 x + 3 y + 3 z = 3 | (equation 2)

{2 x + 5 y = 6 z | (equation 3)

Express the system in standard form:

{2 x + 2 y + 3 z = 3 | (equation 1)

{6 x + 3 y + 3 z = 3 | (equation 2)

{2 x + 5 y - 6 z = 0 | (equation 3)

Swap equation 1 with equation 2:

{6 x + 3 y + 3 z = 3 | (equation 1)

{2 x + 2 y + 3 z = 3 | (equation 2)

{2 x + 5 y - 6 z = 0 | (equation 3)

Subtract 1/3 × (equation 1) from equation 2:

{6 x + 3 y + 3 z = 3 | (equation 1)

{0 x+y + 2 z = 2 | (equation 2)

{2 x + 5 y - 6 z = 0 | (equation 3)

Divide equation 1 by 3:

{2 x + y + z = 1 | (equation 1)

{0 x+y + 2 z = 2 | (equation 2)

{2 x + 5 y - 6 z = 0 | (equation 3)

Subtract equation 1 from equation 3:

{2 x + y + z = 1 | (equation 1)

{0 x+y + 2 z = 2 | (equation 2)

{0 x+4 y - 7 z = -1 | (equation 3)

Swap equation 2 with equation 3:

{2 x + y + z = 1 | (equation 1)

{0 x+4 y - 7 z = -1 | (equation 2)

{0 x+y + 2 z = 2 | (equation 3)

Subtract 1/4 × (equation 2) from equation 3:

{2 x + y + z = 1 | (equation 1)

{0 x+4 y - 7 z = -1 | (equation 2)

{0 x+0 y+(15 z)/4 = 9/4 | (equation 3)

Multiply equation 3 by 4/3:

{2 x + y + z = 1 | (equation 1)

{0 x+4 y - 7 z = -1 | (equation 2)

{0 x+0 y+5 z = 3 | (equation 3)

Divide equation 3 by 5:

{2 x + y + z = 1 | (equation 1)

{0 x+4 y - 7 z = -1 | (equation 2)

{0 x+0 y+z = 3/5 | (equation 3)

Add 7 × (equation 3) to equation 2:

{2 x + y + z = 1 | (equation 1)

{0 x+4 y+0 z = 16/5 | (equation 2)

{0 x+0 y+z = 3/5 | (equation 3)

Divide equation 2 by 4:

{2 x + y + z = 1 | (equation 1)

{0 x+y+0 z = 4/5 | (equation 2)

{0 x+0 y+z = 3/5 | (equation 3)

Subtract equation 2 from equation 1:

{2 x + 0 y+z = 1/5 | (equation 1)

{0 x+y+0 z = 4/5 | (equation 2)

{0 x+0 y+z = 3/5 | (equation 3)

Subtract equation 3 from equation 1:

{2 x+0 y+0 z = (-2)/5 | (equation 1)

{0 x+y+0 z = 4/5 | (equation 2)

{0 x+0 y+z = 3/5 | (equation 3)

Divide equation 1 by 2:

{x+0 y+0 z = (-1)/5 | (equation 1)

{0 x+y+0 z = 4/5 | (equation 2)

{0 x+0 y+z = 3/5 | (equation 3)

Collect results:

 {x = -1/5 , y = 4/5 , z = 3/5

i need a diagram

step-by-step explanation:

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