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?
-$\left\{ \begin{aligned}
x + 6 y & = 18 \
y & = - \frac { 1 } { 6 } x + 3
\end{aligned} \right.$
A) parallel lines; no solution
B) identical lines; infinite number of solutions
C) lines intersecting at a single point; one solution

Question

Quizplus · Accepted Answer

The second equation is in slope-intercept form with slope $ - \frac { 1 } { 6 } $ and $ y $-intercept $ 3 $. So, the graph of the second equation is a line with slope $ - \frac { 1 } { 6 } $ and $ y $-intercept $ 3 $. The first equation is in standard form with $ x $-coefficient $ 1 $ and $ y $-coefficient $ 6 $. So, the graph of the first equation is a line with slope $ - \frac { 1 } { 6 } $ and $ y $-intercept $ 3 $. Therefore, the graphs of the two equations are identical lines, and the system has an infinite number of solutions.

Without Graphing, Decide: (A) Are the Graphs of the Equations {x+6y=18y=−16x+3\left\{ \begin{aligned}x + 6 y & = 18 \\y & = - \frac { 1 } { 6 } x + 3\end{aligned} \right.⎩⎨⎧​x+6yy​=18=−61​x+3​

Without Graphing, Decide:
(A) Are the Graphs of the Equations $\left\{ \begin{aligned}x + 6 y & = 18 \\y & = - \frac { 1 } { 6 } x + 3\end{aligned} \right.$