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?
-$\left\{ \begin{array} { r }
\frac { 1 } { 4 } x - y = 1 \
x = 4
\end{array} \right.$
A)parallel lines; no solution
B)lines intersecting at a single point; one 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?
-$\left\{ \begin{array} { r } 
\frac { 1 } { 4 } x - y = 1 \
x = 4
\end{array} \right.$
A)parallel lines; no solution
B)lines intersecting at a single point; one solution
C)identical lines; infinite number of solutions

Quizplus · Accepted Answer

The second equation, $x = 4$, is a vertical line, and the first equation can be rewritten in slope-intercept form as $y = \frac{1}{4}x - 1$, which is not parallel to $x = 4$. Thus, they intersect at a single point where $x = 4$, leading to one solution.

Without Graphing, Decide: (A)Are the Graphs of the Equations Are {14x−y=1x=4\left\{ \begin{array} { r } \frac { 1 } { 4 } x - y = 1 \\x = 4\end{array} \right.{41​x−y=1x=4​

Without Graphing, Decide:
(A)Are the Graphs of the Equations Are $\left\{ \begin{array} { r } \frac { 1 } { 4 } x - y = 1 \\x = 4\end{array} \right.$