Question 1145499
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<pre>
The intersection point is easy to find : for it, add and subtract the given equations. You will get the intersection point (4,1).


To find its distance from the line 3x + 2y = 5, use this formula


    d = {{{abs(Ap + Bq +C)/sqrt(A^2+B^2)}}},     (1)


which is valid for any point (p,q) in a coordinate plane and any line Ax + By + C = 0.


In your case, p= 4, q= 1, A = 3, B= 2, C= -5,  so the distance is


    d = {{{abs(3*4 + 2*1 - 5)/sqrt(3^2+2^2)}}} = {{{9/sqrt(13)}}} units.
</pre>

Solved.


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Regarding the formula (1), see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Vectors/The-distance-from-a-point-to-a-straight-line-in-a-coordinate-plane.lesson>The distance from a point to a straight line in a coordinate plane</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/HOW-TO-calculate-the-distance-from-a-point-to-a-straight-line-in-a-coordinate-plane.lesson>HOW TO calculate the distance from a point to a straight line in a coordinate plane</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Vectors/Using-formula-for-the-distance-from-a-point-to-a-straight-line-in-a-plane-to-solve-concrete-problems.lesson>Using formula for the distance from a point to a straight line in a plane to solve word problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Vectors/OVERVIEW-of-lessons-on-the-distance-from-a-point-to-a-straight-line-in-a-coordinate-plane.lesson>OVERVIEW of lessons on the distance from a point to a straight line in a coordinate plane</A> 

in this site.