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?
-$\left\{ \begin{aligned}
x + 5 y & = 20 \
y & = - \frac { 1 } { 5 } x + 4
\end{aligned} \right.$
A)identical lines; infinite number of solutions
B)parallel lines; no solution
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 } { 5 } $ and $ y $-intercept $ 4 $. So, the line has a slope of $ - \frac { 1 } { 5 } $ and passes through the point $ (0, 4) $. The first equation is in standard form with $ x $-coefficient $ 1 $ and $ y $-coefficient $ 5 $. So, the line has a slope of $ - \frac { 1 } { 5 } $ and $ y $-intercept $ 4 $. Therefore, the graphs of the equations are identical lines and the system has an infinite number of solutions.

Without Graphing, Decide: (A)Are the Graphs of the Equations Are {x+5y=20y=−15x+4\left\{ \begin{aligned}x + 5 y & = 20 \\y & = - \frac { 1 } { 5 } x + 4\end{aligned} \right.⎩⎨⎧​x+5yy​=20=−51​x+4​

Without Graphing, Decide:
(A)Are the Graphs of the Equations Are $\left\{ \begin{aligned}x + 5 y & = 20 \\y & = - \frac { 1 } { 5 } x + 4\end{aligned} \right.$