2. What is the sum of the three solutions (find the values for x, y, and z, then add the answers)? 2x + 3y − z = 5 x
− 3y + 2z = −6
3x + y − 4z = −8
please show steps

x = 30/7 , y = 46/7 , z = 48/7

Step-by-step explanation:

Solve the following system:

{2 x + 3 y - z = 5 x | (equation 1)

2 z - 3 y = -6 | (equation 2)

3 x + y - 4 z = -8 | (equation 3)

Express the system in standard form:

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

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

3 x + y - 4 z = -8 | (equation 3)

Add equation 1 to equation 3:

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

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

0 x+4 y - 5 z = -8 | (equation 3)

Swap equation 2 with equation 3:

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

0 x+4 y - 5 z = -8 | (equation 2)

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

Add 3/4 × (equation 2) to equation 3:

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

0 x+4 y - 5 z = -8 | (equation 2)

0 x+0 y - (7 z)/4 = -12 | (equation 3)

Multiply equation 3 by -4:

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

0 x+4 y - 5 z = -8 | (equation 2)

0 x+0 y+7 z = 48 | (equation 3)

Divide equation 3 by 7:

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

0 x+4 y - 5 z = -8 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Add 5 × (equation 3) to equation 2:

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

0 x+4 y+0 z = 184/7 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Divide equation 2 by 4:

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

0 x+y+0 z = 46/7 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Subtract 3 × (equation 2) from equation 1:

{-(3 x) + 0 y - z = -138/7 | (equation 1)

0 x+y+0 z = 46/7 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Add equation 3 to equation 1:

{-(3 x)+0 y+0 z = -90/7 | (equation 1)

0 x+y+0 z = 46/7 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Divide equation 1 by -3:

{x+0 y+0 z = 30/7 | (equation 1)

0 x+y+0 z = 46/7 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Collect results:

{x = 30/7 , y = 46/7 , z = 48/7

add the numbers under frequency to find the total number:

5 + 8 +7 + 4 + 0 +1 = 25

the answer is 25.