Question 940705
You can get the slope of the lines since you have the formula for each point. 
Assume {{{t=1}}} then the change in y is 3, change in x is 4 so the slope is,
{{{m=3/4}}}
So line 1 is, using the point-slope form,
{{{y-2=(3/4)(x-1)}}}
{{{y-2=(3/4)x-3/4}}}
{{{y=(3/4)x+5/4}}}
Similarly for line 2,
{{{y-(-1)=2(x-2)}}}
{{{y+1=2x-4}}}
{{{y=2x-5}}}
For intersection, set the two equal to each other.
{{{(3/4)x+5/4=2x-5}}}
{{{3x+5=8x-20}}}
{{{-5x=-25}}}
{{{x=5}}
Then,
{{{y=2(5-5}}}
{{{y=5}}}
(5,5)
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{{{drawing(300,300,-3,8,-3,8,grid(1),circle(1,2,0.2),circle(2,-1,0.2),circle(5,5,0.2),graph(300,300,-3,8,-3,8,(3/4)x+5/4,2x-5))}}}