Question 548001
the equations represent a parabola and a straight line, looking like this: {{{graph(300,300,-3,7,-9,21,2x^2-4x-5,3x+1)}}}
{{{3x-y=1}}} ---> {{{y=3x-1}}}
Substituting that expression in the other equation, we get
{{{2x^2-4x-5=3x-1}}} --> {{{2x^2-7x-4=0}}}
Then, applying the quadratic formula, we find
{{{x= (7 +- sqrt( 7^2-4*2*(-4) ))/(2*2)=(7 +- sqrt( 49+32))/4=(7 +- sqrt(81))/4 =(7 +- 9)/4 }}}
So the answers are {{{x=-1/2}}} and {{{x=4}}}
Substituting into {{{y=3x-1}}}, we find
for {{{x=-1/2}}} --> {{{y=3*(-1/2)-1=-3/2-2/2=-5/2}}}
for {{{x=4}}} --> {{{y=3*4-1=12-1=11}}}
So the answers are points (-1/2,-5/2) and (4,11).