Answered

Which of the following best describes the

graph of the system of equations shown

below?

6x − 14y = −28

3y − 7x = −14

A The lines are parallel.

B The lines are the same.

C The lines intersect but are not

perpendicular.

D The lines intersect and are perpendicular.

Verified Answer :

\(k:6x-14y=-28\ \ \ \ |subtract\ 6x\ from\ both\ sides\\\\-14y=-6x-28\ \ \ \ \ \ |divide\ both\ sides\ by\ (-14)\\\\y=\frac{-6}{-14}x-\frac{28}{-14}\\\\y=\frac{3}{7}x+2\\----------------------------\\l:3y-7x=-14\ \ \ \ \ |add\ 7x\ to\ both\ sides\\\\3y=7x-14\ \ \ \ \ \ |divide\ both\ sides\ by\ 3\\\\y=\frac{7}{3}x-\frac{14}{3}\)

\(Two\ lines\ are\ perpendicular\ if\ product\ of\ the\ slopes\ is\ equal\ -1.\\\\k:y=\frac{3}{7}x+2\to the\ skolpe\ m_k=\frac{3}{7}\\\\l:y=\frac{7}{3}x-\frac{14}{3}\to the\ slope\ m_l=\frac{7}{3}\\\\m_k\times m_l=\frac{3}{7}\times\frac{7}{3}=1 eq-1\\\\conclusion:the\ lines\ are\ not\ perpendicular\\\\Two\ lines\ are\ parallel\ if\ the\ slopes\ are\ equal.\\\\m_k=\frac{3}{7};\ m_l=\frac{7}{3}\to m_k eq m_l\\\\conclusion:the\ lines\ are\ not\ parallel\)


\(Answer:\boxed{C-The\ lines\ intersect\ but\ are\ not\ perpendicular.}\)

xXxGirxXx

First, you want to find out what the slope and the y-intercept is, you must put both equations in y=mx+b from.

6x − 14y = −28                    :First, subtract the 6x over to the right
-6x                   -6x

(-14y = -6x - 28) ÷ -14         :Then, divide the whole equation by -14

y = 6/14x + 2                        :Now, reduce the fraction, divide both the top and the                                                 bottom by 2

y = 3/7x + 2

3y − 7x = −14                      :First, add the 7x over to the right side
      +7x          +7x

(3y = 7x - 14) ÷ 3                 :Next, divide the whole equation by 3

y = 7/3x - 14/3


y = 3/7x + 2             slope: 3/7     y-int.: 2

y = 7/3x - 14/3         slope: 7/3     y-int.: -14/3 or -4 7/10 or -4.7

C.  Your answer is C.  They will eventually intersect, but not at a right angle.

Related Questions