Solve the following system. 2x-y=5 , x+3y = 12

2x-y = 5..(1) and x+3y =
12...(2).

We solve the equations using the analytic
geometry.

Here, we a have two linear equations in x and y.
We have to solve for the values of x and y. We recast both equations in the
slope intercept form, like:  y = max+c.

2x-y= 5 => y
= 2x-5....................................(1).

x+3y = 12
=> y = -(1/3)x + 4......................(2).

We can
Easily see that the slopes of the two equations are not same. So they are not parallel.
So the equations representing two non parallel lines definitely intesect  giving some
definite solutions.

At the point of intersection, y
coordinates are same. So we equate the right sides of the equations (1) and (2) and
solve for x (or coordinate).

2x-5 =
-(1/3)x+4.

(2+1/3)x =
5+4.

7x/3 = 9.

(7x/3)*(3/7) =
9*3/7 =
27/7.

x= 27/7.

Therefore,
using  the first equation, y = 2x-5, where we put x = 27/7, we get: y = 2(27/7) - 5 =
19/7.

Therefore x= 27/7 and y =
19/7.