Find the point of intersection of the lines; ?

Question

3x-y-7 =0

x+5y+3 =0

Answer 1

solve for x and y

3x-y-7 =0  ---(1)

x+5y+3 =0  ---(2)

From (1) and (2)

3x - y = 7  

3x+15y = -9    

After subtracting

16y = -9 - 7 = -16 or y = -1

or x = - 3 -5y = 5 -3 =2

Intersects at (2, -1)

Answer 2

For finding the points of intersection of two lines, solve the equations of lines together for unknowns x & y.

In this case,

3x-y-7=0

&

x+5y+3=0

By multiplying the second equation by 3 & subtracting the result from 1'st equation, we get

-16y-16=0

->y = -1

Substituting the value of y in 1'st equation,

3x-(-1)-7=0

->3x-6=0

->x=2

Therefore, point of intersection is (x,y) = (2,-1)