Answer :
Answer:
y=15-3z
x=-5.25-0.25z
Step-by-step explanation:
You are given the system of two equations with three variables:
[tex]\left\{\begin{array}{l}4x-2y-5z=-51\\ \\4x-y-2z=-36\end{array}\right.[/tex]
Write the augmented matrix for this system of equations
[tex]\left(\begin{array}{ccccc}4&-2&-5&|&-51\\4&-1&-2&|&-36\end{array}\right)[/tex]
Now, find the reduced row-echelon form of the augmented matrix for this system of equations. Subtract the second row from the first row:
[tex]\left(\begin{array}{ccccc}4&-2&-5&|&-51\\0&-1&-3&|&-15\end{array}\right)[/tex]
You get the system of two equations:
[tex]\left\{\begin{array}{r}4x-2y-5z=-51\\ \\-y-3z=-15\end{array}\right.[/tex]
From the second equation
[tex]y=15-3z[/tex]
Substitute it into the first one:
[tex]4x-2(15-3z)-5z=-51\\ \\4x-30+6z-5z=-51\\ \\4x=-21-z\\ \\x=-\dfrac{21}{4}-\dfrac{1}{4}z\\ \\x=-5.25-0.25z[/tex]