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?
-$\left\{ \begin{array} { l }
2 x + y = - 7 \
4 x + 5 y = - 5
\end{array} \right.$
A)identical lines; infinite number of solutions
B)parallel lines; no solution
C)lines intersecting at a single point; one solution

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?
-$\left\{ \begin{array} { l } 
2 x + y = - 7 \
4 x + 5 y = - 5
\end{array} \right.$
A)identical lines; infinite number of solutions
B)parallel lines; no solution
C)lines intersecting at a single point; one solution

Quizplus · Accepted Answer

C)lines intersecting at a single point; one solution.The slopes of the lines are different (first equation has a slope of -2, second has a slope of -4/5), indicating they are not parallel or identical, thus they must intersect at a single point. This means the system has exactly one solution.

Without Graphing, Decide: (A)Are the Graphs of the Equations Are {2x+y=−74x+5y=−5\left\{ \begin{array} { l } 2 x + y = - 7 \\4 x + 5 y = - 5\end{array} \right.{2x+y=−74x+5y=−5​

Without Graphing, Decide:
(A)Are the Graphs of the Equations Are $\left\{ \begin{array} { l } 2 x + y = - 7 \\4 x + 5 y = - 5\end{array} \right.$