# Math Help - What is the intersection of the following lines...

1. ## What is the intersection of the following lines...

y - 3x + 2 = 0

and

-3x + 4y -1 = 0

Thanks!

2. Originally Posted by gobbajeezalus
y - 3x + 2 = 0

y = 3x - 2

and

-3x + 4y -1 = 0

4y = 3x + 1

y = (3x + 1)/4

Thanks!
set the two expressions that equal y equal to each other. solve for x, then determine the value of y.

Originally Posted by gobbajeezalus
y - 3x + 2 = 0

and

-3x + 4y -1 = 0

Thanks!

y-3x=-2
4y-3x=1 (you change the signs on one of the lines and the x's go)

-y+3x=2
4y-3x=1

3y=3 y=1

now you fill in for y

y-3x=-2

(1)-3x=-2

-3x=-3 -x=-1 x=1

there for (1,1) are the points

4. Originally Posted by gobbajeezalus
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

$(1) y-3x+2=0$

$(2)-3x+4y-1=0$

Isolate y in the first equation

$y=3x-2$

Plug that value into the second equation and solve for $x$

$-3x+4(3x-2)-1=0$

$
-3x+12x-8-1=0$

$9x=9$

$x=1$

Plug that value of x into equation 1 and solve for y

$
y-3(1)+2=0$

$y-1=0$

$y=1$

$\therefore$ the intersection of the lines occurs at point $(1,1)$