Answer:
d= 2.4961508830135313
Step-by-step explanation:
First find the intersection of x+y=5 and x–y=3
Add the equations
x+y=5
x–y=3
----------------
2x = 8
Divide by 2
2x/2 = 8/2
x = 4
Subtract the equations
x+y=5
- x+y=-3
------------------
2y = 2
y=1
(4,1)
We need to know the distance from the line 3x+2y=5 and the point (4,1)
Rewritng the equation of the line
3x+2y -5=0
The formula for the distance is
| ax1+by1+c|
d= ------------------- where a b and c are the coefficients on the line
sqrt( a^2+b^2)
| 3*4+2*1+-5|
d= -------------------
sqrt( 3^2 +2^2)
| 12+2-5|
d= -------------------
sqrt( 9+4)
9
d= -------------------
sqrt(13)
d= 2.4961508830135313
