At what point does the graph of the parametric equations x=3-2t y=-2+5t intersect the graph of the parametric equations x=-1+3s y=5-9s? The answer is the point of intersection(x,y).

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Answer 1 · 2018-06-13T17:47:34

$(- 7, 23)$ $(-7,23)$

$t = \frac{3 - x}{2} \Rightarrow y_{1} = - 2 + 5 \cdot \frac{3 - x}{2}$ $t = (3 - x)/2 => y_1 = -2 + 5 * (3 - x)/2$

$s = \frac{x + 1}{3} \Rightarrow y_{2} = 5 - 3 (x + 1)$ $s = (x + 1)/3 => y_2 = 5 - 3(x + 1)$

$y_{1} = y_{2} \Rightarrow$ $y_1 = y_2 =>$

$- 2 + 5 \cdot \frac{3 - x}{2} = 5 - 3 x - 3$ $-2 + 5 * (3 - x)/2 = 5 - 3x - 3$

$- 4 + 5 (3 - x) = 4 - 6 x$ $-4 + 5(3 - x) = 4 - 6x$

$15 - 5 x = 8 - 6 x$ $15 - 5x = 8 - 6x$

$x = 8 - 15 = - 7$ $x = 8 - 15 = -7$

$y_{2} = 5 - 3 (- 6) = 5 + 18 = 23$ $y_2 = 5 - 3(-6) = 5 + 18 = 23$