Find the x- and y- coordinates of the point of intersection of the lines

Question

− x + 2 y  =  − 3
 3 x +  y  =  2

Answer 1

Givel Line Equations

− x + 2 y  =  − 3  ---------------> (1)
 3 x +  y  =  2 ------------------> (2)

Multiply equation (1) with 3 and add to equation (2)

-3x + 6y  =  -9

 3x + y  =  2

________________

  0 + 7y  =  -7

7y  =  -7

y  =  -7 / 7

y  =  - 1

Substitute y = -1 in equation (2)

3x + (-1)  =  2

3x - 1  =  2

3x = 2 + 1

x  =  3/3

x  =  1

Answer :

At point (x,y) = (1,-1) the two lines intersect each other.