The lines x+y = 10 and -3x+y = 2 have a unique solution. What is the distance (in units) between the unique solution and the point of intersection of the line x+y = 10 and the x-axis?

Correct option is A

Given:
Linear equation are x+y = 10 and -3x+y = 2
Formula Used:
Distance = $$\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2 }$$​​
If line cut x-axis , then y=0
Solution:
Point of intersection of x+y = 10 and -3x+y = 2 is:
x=10-y …..(1)
-3x+y=2 …..(2)
Putting the value of x in eq(2)
-3(10-y) +y =2
-30 +3y + y =2
4y= 2+30
y=8
And
x= 10- 8 = 2
Point is (2,8)
The point where x+y=10 cuts x-axis
Then the point where line cut x-axis is the pint where y=0;
x+y=10
x+0=10
x=10
Point is (10,0)    

Distance, 
 $$\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2 )} \\\ \\=\sqrt{(10-2)^2 +(0 -8)^2 )} \\\ \\=\sqrt{(64+64 )}=8√2$$​​