Answered

Explore a wide range of topics and get answers from experts on IDNLearn.com. Join our knowledgeable community and get detailed, reliable answers to all your questions.

Type the correct answer in each box. If necessary, use / for the fraction bar.

Find the solution to this system of equations.

[tex]\[
\begin{array}{l}
x + y = 1 \\
2x - y + z = 1 \\
x + 2y + z = \frac{8}{3} \\
x = \square \\
y = \square \\
z = \square
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To find the solution to the system of equations:

[tex]\[ \begin{array}{l} x + y = 1 \\ 2x - y + z = 1 \\ x + 2y + z = \frac{8}{3} \\ \end{array} \][/tex]

we solve this system step-by-step. The variables [tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( z \)[/tex] that satisfy all three equations are:

[tex]\[ x = \frac{1}{3} \][/tex]

[tex]\[ y = \frac{2}{3} \][/tex]

[tex]\[ z = 1 \][/tex]

So, filling these into the blanks:

[tex]\[ \begin{array}{l} x = \frac{1}{3} \\ y = \frac{2}{3} \\ z = 1 \\ \end{array} \][/tex]

Thus, the solution to the given system of equations is:

[tex]\[ x = \boxed{\frac{1}{3}} \][/tex]

[tex]\[ y = \boxed{\frac{2}{3}} \][/tex]

[tex]\[ z = \boxed{1} \][/tex]
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.