Solve the given set of equations for value of x:

x-3z=-5

2x-y+2z=16

7x-3y-5z=19

x-3z=-5

2x-y+2z=16

7x-3y-5z=19

djeljenike
2021-02-23
Answered

Solve the given set of equations for value of x:

x-3z=-5

2x-y+2z=16

7x-3y-5z=19

x-3z=-5

2x-y+2z=16

7x-3y-5z=19

You can still ask an expert for help

Brittany Patton

Answered 2021-02-25
Author has **100** answers

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

$z=\frac{26+y}{8}$ ...(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

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

3y=52+2y-54

3y-2y=-2

y=-2

Step 4

Substitute y = -2 in equation (v)

$z=\frac{26+y}{8}$

$z=\frac{26-2}{8}$

$z=\frac{24}{8}$

z=3

Step 5

Substitute z = 3 inequation (iv)

x=3z-5

$x=3\times 3-5$

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

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

3y=52+2y-54

3y-2y=-2

y=-2

Step 4

Substitute y = -2 in equation (v)

z=3

Step 5

Substitute z = 3 inequation (iv)

x=3z-5

x=9-5

x=4

Step 6

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

Jeffrey Jordon

Answered 2021-11-20
Author has **2027** answers

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