Question

Find a solution to the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations 4x-2y-5z=-51 4x-y-2z=-36

Answer 1

Answer:

y=15-3z

x=-5.25-0.25z

Step-by-step explanation:

You are given the system of two equations with three variables:

$\left\{\begin{array}{l}4x-2y-5z=-51\\ \\4x-y-2z=-36\end{array}\right.$

Write the augmented matrix for this system of equations

$\left(\begin{array}{ccccc}4&-2&-5&|&-51\\4&-1&-2&|&-36\end{array}\right)$

Now,  find the reduced row-echelon form of the augmented matrix for this system of equations. Subtract the second row from the first row:

$\left(\begin{array}{ccccc}4&-2&-5&|&-51\\0&-1&-3&|&-15\end{array}\right)$

You get the system of two equations:

$\left\{\begin{array}{r}4x-2y-5z=-51\\ \\-y-3z=-15\end{array}\right.$

From the second equation

$y=15-3z$

Substitute it into the first one:

$4x-2(15-3z)-5z=-51\\ \\4x-30+6z-5z=-51\\ \\4x=-21-z\\ \\x=-\dfrac{21}{4}-\dfrac{1}{4}z\\ \\x=-5.25-0.25z$