Without graphing, decide:
(a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point?
(b) How many solutions does the system have?
-$\left\{ \begin{array} { r }
\frac { 1 } { 6 } x - y = 1 \
x = 6
\end{array} \right.$
A) lines intersecting at a single point; one solution
B) parallel lines; no solution
C) identical lines; infinite number of solutions

Question

Without graphing, decide:
(a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point?
(b) How many solutions does the system have?
-$\left\{ \begin{array} { r } 
\frac { 1 } { 6 } x - y = 1 \
x = 6
\end{array} \right.$
A) lines intersecting at a single point; one solution
B) parallel lines; no solution
C) identical lines; infinite number of solutions

Quizplus · Accepted Answer

The first equation can be rewritten as $x = 6y + 6$. The second equation is $x = 6$. Substituting $x = 6$ into the first equation gives $6 = 6y + 6$, which simplifies to $y = 0$. Thus, the lines intersect at the point (6, 0), indicating one solution.

Without Graphing, Decide: (A) Are the Graphs of the Equations {16x−y=1x=6\left\{ \begin{array} { r } \frac { 1 } { 6 } x - y = 1 \\x = 6\end{array} \right.{61​x−y=1x=6​

Without Graphing, Decide:
(A) Are the Graphs of the Equations $\left\{ \begin{array} { r } \frac { 1 } { 6 } x - y = 1 \\x = 6\end{array} \right.$