SOLUTION: Find the point of intersection of the lines 2x-3y+1=0 and 4y+ 3x +2=0

Algebra ->  Points-lines-and-rays -> SOLUTION: Find the point of intersection of the lines 2x-3y+1=0 and 4y+ 3x +2=0      Log On


   

Question 407967: Find the point of intersection of the lines 2x-3y+1=0 and 4y+ 3x +2=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2x-3y%2B1=0 and 4y%2B+3x+%2B2=0

slope-intercept form:
y=%282%2F3%29x%2B1%2F3 and y=+-%283%2F4%29x+-1%2F2
graph:

The point (x, y) where they meet must lie on both lines, so x and y must satisfy both equations.
So we are looking to solve the two simultaneous equations
y=%282%2F3%29x%2B1%2F3 and y=+-%283%2F4%29x+-1%2F2... left sides are same, so right sides must be same too
%282%2F3%29x%2B1%2F3=-%283%2F4%29x+-1%2F2...solve for x
%282%2F3%29x%2B%283%2F4%29x=-1%2F3+-1%2F2
x%282%2F3%2B3%2F4%29=+-1%2F3+-1%2F2
x%288%2B9%29%2F12=+%28-2-3%29%2F6
17x=+cross%2812%292%28-5%29%2Fcross%286%29
17x=+2%28-5%29
17x=+-10
x=+-10%2F17
x=+-0.59

y=%282%2F3%29%28-0.59%29%2B1%2F3
y=-0.39%2B0.33
y=-0.06


The point (x, y) is (-0.59, -0.06)
check:
2x-3y%2B1=0
2%28-0.59%29-3%28-0.06%29%2B1=0
-1.18%2B0.18+%2B1=0
-1%2B1=0
0=0.......x and y must satisfy this equation...check the other one