Question 131635
ok the intersection means in math where the two lines intersect each other.
so the point of the intersection staisfied both equation.
y=x " equation one"
4x+5y=9 " equation two"
so we can solve this by three ways Elimination or Sub. or graphying
i am going to do it by substution ok
so now , sub equation one in equation two 
instead of y put x in the second equation
4x+5(X)=9
9x=9 divde both sides by 9
 x=1 use either first or second equation to get the Y value  because we looking for a point with both corodinates ok. since as i said at the beginning the point of intersection will statifeid both equation so no problems to sub. the value of X in either of these two equation 
the first is easier
y=x
so we got x=1 therfore the y=1 
so the point of the intersection is (1,1) Good Luck 
try to sub the value of X in the second equatiion to find a surpise! the same answer for Y