Solve the system by substitution. Substitute the expression in the second equation into the first equation and solve. If the lines coincide, answer dependent . If the lines are parallel, answer no solution .
D)dependent
E)no solution

Question

Solve the system by substitution. Substitute the expression in the second equation into the first equation and solve.  If the lines coincide, answer dependent . If the lines are parallel, answer no solution .
D)dependent 
E)no solution

Quizplus · Accepted Answer

The system is given by:
\begin{align*}
y&=\frac{1}{3}x-2\
3y&=x-6\
\end{align*}
Substituting $3y$ for $x$ in the first equation, we get:
\begin{align*}
y&=\frac{1}{3}(3y+6)-2\
y&=y+2-2\
y&=y\
\end{align*}
This means any value of $y$ will satisfy the equations, so the system has infinitely many solutions and is dependent. Therefore, the answer is (E) no solution.

Solve the System by Substitution