Step 1

Given the system of equations

x-3z=-5...(i)

2x-y+2z=16...(ii)

7x-3y-5z=19...(iii)

Step 2

Now, solving the equations

Form equation (i)

x-3z=-5

x=3z-5...(iv)

Substitute x=3z-5 in equation (ii)

2x-y+2z=16

2(3z-5)-y+2z=16

6z-10-y+2z=16

8z=16+10+y

\(\displaystyle{z}={\frac{{{26}+{y}}}{{{8}}}}\)...(v)

Step 3

Substitute the value of x from equation (iv) to equation (iii)

7x-3y-5z=19

7(3z-5)-3y-5z=19

21z-35-3y-5z=19

16z3y=19+35

3y=16z-54

\(\displaystyle{3}{y}={16}{\left({\frac{{{26}+{y}}}{{{8}}}}\right)}-{54}\)

3y=52+2y-54

3y-2y=-2

y=-2

Step 4

Substitute y = -2 in equation (v)

\(\displaystyle{z}={\frac{{{26}+{y}}}{{{8}}}}\)

\(\displaystyle{z}={\frac{{{26}-{2}}}{{{8}}}}\)

\(\displaystyle{z}={\frac{{{24}}}{{{8}}}}\)

z=3

Step 5

Substitute z = 3 inequation (iv)

x=3z-5

\(\displaystyle{x}={3}\times{3}-{5}\)

x=9-5

x=4

Step 6

Answer: The value of x for the given system of equations is 4.

Given the system of equations

x-3z=-5...(i)

2x-y+2z=16...(ii)

7x-3y-5z=19...(iii)

Step 2

Now, solving the equations

Form equation (i)

x-3z=-5

x=3z-5...(iv)

Substitute x=3z-5 in equation (ii)

2x-y+2z=16

2(3z-5)-y+2z=16

6z-10-y+2z=16

8z=16+10+y

\(\displaystyle{z}={\frac{{{26}+{y}}}{{{8}}}}\)...(v)

Step 3

Substitute the value of x from equation (iv) to equation (iii)

7x-3y-5z=19

7(3z-5)-3y-5z=19

21z-35-3y-5z=19

16z3y=19+35

3y=16z-54

\(\displaystyle{3}{y}={16}{\left({\frac{{{26}+{y}}}{{{8}}}}\right)}-{54}\)

3y=52+2y-54

3y-2y=-2

y=-2

Step 4

Substitute y = -2 in equation (v)

\(\displaystyle{z}={\frac{{{26}+{y}}}{{{8}}}}\)

\(\displaystyle{z}={\frac{{{26}-{2}}}{{{8}}}}\)

\(\displaystyle{z}={\frac{{{24}}}{{{8}}}}\)

z=3

Step 5

Substitute z = 3 inequation (iv)

x=3z-5

\(\displaystyle{x}={3}\times{3}-{5}\)

x=9-5

x=4

Step 6

Answer: The value of x for the given system of equations is 4.