Question 1048549

{{{Ax + By = C}}}.........      (1)
{{{Dx + Ey = F }}}........     (2)

(a)     Write the slope of the line determined by equation (1)
{{{Ax + By = C}}}.....solve for {{{y}}}
{{{By = -Ax +C}}}
{{{y = -(A/B)x +C/B}}}
the slope is {{{ -(A/B)}}}.....restriction:{{{B<>0}}}

(b)     Write the slope of the line determined by equation (2)
{{{Dx + Ey = F }}}
{{{ Ey = -Dx+F }}}
{{{ y = -(D/E)x+F/E }}}
the slope is {{{ -(D/E)}}}.....restriction:{{{E<>0}}}

(c)     What must be true about the given coefficients to guarantee that the
system is consistent?

A consistent system is a system that has at least one solution.
There will be exactly one unique solution if the coefficient of {{{x}}} and {{{y}}} is not {{{0}}}

means, if {{{ -(A/B)<>0}}} and {{{ -(D/E)<>0}}}