y - 3x + 2 = 0
and
-3x + 4y -1 = 0
Thanks!
The easiest thing to do when to already have a variable isolated (in this case y) is to use the method of substitution
$\displaystyle (1) y-3x+2=0$
$\displaystyle (2)-3x+4y-1=0$
Isolate y in the first equation
$\displaystyle y=3x-2$
Plug that value into the second equation and solve for $\displaystyle x$
$\displaystyle -3x+4(3x-2)-1=0$
$\displaystyle
-3x+12x-8-1=0$
$\displaystyle 9x=9$
$\displaystyle x=1$
Plug that value of x into equation 1 and solve for y
$\displaystyle
y-3(1)+2=0$
$\displaystyle y-1=0$
$\displaystyle y=1$
$\displaystyle \therefore$ the intersection of the lines occurs at point $\displaystyle (1,1)$