2x - 5y + z = 5
3x + 2y - 2 = 17
4x - 3y + 2z = 17
?

x = 17/3 , y = 1 , z = -4/3

Step-by-step explanation:

Solve the following system:

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

-2 + 3 x + 2 y = 17 | (equation 2)

4 x - 3 y + 2 z = 17 | (equation 3)

Express the system in standard form:

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

3 x + 2 y+0 z = 19 | (equation 2)

4 x - 3 y + 2 z = 17 | (equation 3)

Swap equation 1 with equation 3:

{4 x - 3 y + 2 z = 17 | (equation 1)

3 x + 2 y+0 z = 19 | (equation 2)

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

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

{4 x - 3 y + 2 z = 17 | (equation 1)

0 x+(17 y)/4 - (3 z)/2 = 25/4 | (equation 2)

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

Multiply equation 2 by 4:

{4 x - 3 y + 2 z = 17 | (equation 1)

0 x+17 y - 6 z = 25 | (equation 2)

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

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

{4 x - 3 y + 2 z = 17 | (equation 1)

0 x+17 y - 6 z = 25 | (equation 2)

0 x - (7 y)/2+0 z = (-7)/2 | (equation 3)

Multiply equation 3 by -2/7:

{4 x - 3 y + 2 z = 17 | (equation 1)

0 x+17 y - 6 z = 25 | (equation 2)

0 x+y+0 z = 1 | (equation 3)

Subtract 1/17 × (equation 2) from equation 3:

{4 x - 3 y + 2 z = 17 | (equation 1)

0 x+17 y - 6 z = 25 | (equation 2)

0 x+0 y+(6 z)/17 = (-8)/17 | (equation 3)

Multiply equation 3 by 17/2:

{4 x - 3 y + 2 z = 17 | (equation 1)

0 x+17 y - 6 z = 25 | (equation 2)

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

Divide equation 3 by 3:

{4 x - 3 y + 2 z = 17 | (equation 1)

0 x+17 y - 6 z = 25 | (equation 2)

0 x+0 y+z = (-4)/3 | (equation 3)

Add 6 × (equation 3) to equation 2:

{4 x - 3 y + 2 z = 17 | (equation 1)

0 x+17 y+0 z = 17 | (equation 2)

0 x+0 y+z = -4/3 | (equation 3)

Divide equation 2 by 17:

{4 x - 3 y + 2 z = 17 | (equation 1)

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

0 x+0 y+z = -4/3 | (equation 3)

Add 3 × (equation 2) to equation 1:

{4 x + 0 y+2 z = 20 | (equation 1)

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

0 x+0 y+z = -4/3 | (equation 3)

Subtract 2 × (equation 3) from equation 1:

{4 x+0 y+0 z = 68/3 | (equation 1)

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

0 x+0 y+z = -4/3 | (equation 3)

Divide equation 1 by 4:

{x+0 y+0 z = 17/3 | (equation 1)

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

0 x+0 y+z = -4/3 | (equation 3)

Collect results:

 {x = 17/3 , y = 1 , z = -4/3

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2