Question 323821
#1:
1.{{{ y = 6x^2 - 5x}}}
2.{{{    y = 2x + 3}}}
Since they both equal y, set them equal to each other.
{{{6x^2-5x=2x+3}}}
{{{6x^2-7x-3=0}}}
{{{(2x-3)(3x+1)=0}}}
Two solutions:
{{{2x-3=0}}}
{{{2x=3}}}
{{{x=3/2}}}
The use either equation to solve for y,
{{{y=2(3/2)+3=6}}}
(3/2,6)
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{{{3x+1=0}}}
{{{3x=-1}}}
{{{x=-1/3}}}
{{{y=2(-1/3)+3=9/3-2/3=7/3}}}
(-1/3,7/3)
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{{{drawing(300,300,-5,5,-2,8,grid(1),circle(3/2,6,.2),circle(-1/3,7/3,.2),graph(300,300,-5,5,-2,8,6x^2-5x,2x+3))}}}
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#2: Same approach
1.{{{ y = x^2 - 3x -3}}}
2.{{{y = -x^2 + 5x + 7}}}
{{{x^2-3x-3=-x^2+5x+7}}}
{{{2x^2-8x-10=0}}}
{{{x^2-4x-5=0}}}
{{{(x-5)(x+1)=0}}}
Two solutions:
{{{x-5=0}}}
{{{x=5}}}
{{{y=(5)^2-3(5)-3=7}}}
(5,7)
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{{{x+1=0}}}
{{{x=-1}}}
{{{y=(1)^2-3(-1)-3=1}}}
(-1,1)
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{{{drawing(300,300,-5,11,-5,11,grid(1),circle(5,7,.3),circle(-1,1,.3),graph(300,300,-5,11,-5,11,x^2-3x-3,-x^2 + 5x + 7))}}}