Solve the given set of equations for value of x: x-3z=-5 2x-y+2z=16 7x-3y-5z=19

Solve the given set of equations for value of x:
x-3z=-5
2x-y+2z=16
7x-3y-5z=19

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Brittany Patton
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.
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