Question 1196067
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Find the coordinates of the point where the line (x,y) = (3+2t, -1+3t) meets the line y=2x+5 .
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<pre>
We want to find "t" such that

    x = 3 + 2t,

    y = -1 + 3t


For it, we substitute these expressions into equation y = 2x + 5.  It gives us

    -1 + 3t = 2*(3+2t) + 5.


Simplify and find "t"

    -1 + 3t = 6 + 4t + 5

    -1 - 6 - 5 = 4t - 3t

        -12    =   t.


Then the point's coordinates are  

    x = 3+2t = 3 + 2*(-12) = -21;  

    y = -1 + 3t = -1 + 3*(-12) = -37.


<U>ANSWER</U>.  The intersection point is (-21,-37).
</pre>

Solved.