Question

Solve the system of equations 3y + 2z = 12 and y – z= 9.

Answer 1

`\left\{\begin{array}{ccc}3y+2z=12\\y-z=9&|multiply\ both\ sides\ by\ 2\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3y+2z=12\\2y-2z=18\end{array}\right}\\.\ \ \ \ 5y=30\ \ \ |divide\ both\ sides\ by\ 5\\.\ \ \ \ y=6\\\\subtitute\ the\ value\ of\ y\ to\ the\ equation\ y-z=9\\\\6-z=9\ \ \ |subtract\ 6\ from\ both\ sides\\-z=3\ \ \ |change\ signs\\z=-3\\\\Answer:\left\{\begin{array}{ccc}y=6\\z=-3\end{array}\right`