2x+4y=11 and -5x+3y=5

Question

find the intersection of the lines

Answer 1

solve as a system of 2 equations.

extract value of x from the 1st equation:

2x+4y=11

2x=11-4y

x=5.5-2y

plug this value of x in second equation:

-5x+3y=5

-5(5.5-2y)+3y=5

-27.5+10y+3y=5

-27.5+13y=5

13y=32.5

y=2.5

x=5.5-2y=5.5-2*5=0.5

So, these 2 lines cross each other in (0.5, 2.5)