Question

Solve{(x,+,3y,=,8),(2y,=,x,+,6):}

Systems of equations
ANSWERED
asked 2020-12-27

Solve \(\displaystyle{\left\lbrace\begin{matrix}{x}&+&{3}{y}&=&{8}\\{2}{y}&=&{x}&+&{6}\end{matrix}\right.}\)

Expert Answers (1)

2020-12-28

\(\displaystyle{\left\lbrace\begin{matrix}{x}&+&{3}{y}&=&{8}\\{2}{y}&=&{x}&+&{6}\end{matrix}\right.}\)

Rewrite equation (2) in standart form NSK

2y – x = 6

Add equation (1) and (3) 

5y = 14

Solve for y 

\(\displaystyle{y}=\frac{14}{{5}}\)

Substitute \(\displaystyle{y}=\frac{14}{{5}}\) into equation (1) and solve for x NSK

\(\displaystyle{x}={3}{\left(\frac{14}{{5}}\right)}={8}\)

\(\displaystyle{x}+\frac{42}{{5}}={8}\)

\(\displaystyle{x}={8}–\frac{42}{{5}}\)

\(\displaystyle{x}=\frac{{{40}–{42}}}{{5}}\)

\(\displaystyle{x}=-\frac{2}{{5}}\)

Thus, the solution is \(\displaystyle{\left(-\frac{2}{{5}};\frac{14}{{5}}\right)}\)

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