Use back-substitution to solve the system of linear equations.\begin{cases}x &-y &+5z&=26\\ &\ \ \ y &+2z &=1 \\ & &\ \ \ \ \ z & =6\end{cases}(x,y,z)=()

FobelloE

FobelloE

Answered question

2021-03-15

Use back-substitution to solve the system of linear equations.
{xy+5z=26   y+2z=1     z=6
(x,y,z)=()

Answer & Explanation

Corben Pittman

Corben Pittman

Skilled2021-03-17Added 83 answers

Step 1
The system of the linear equations is given by
x-y+5z=26...(1)
y+2z=1...(2)
z=6...(3)
To evaluate : The solution of the system of the linear equations
Step 2
Substitute the value of z from equation (3) into equation (2) we get,
y+2×6=1
y+12=1
y=11
Now, substitute the values of y and z in equation (1) we get,
x(11)+5×6=26
x+11+30=26
x+41=26
x=2641
x=15
Hence, the solution of the stem of the linear equations is (x,y,z)=(-15,-11,6)

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