# Thread: 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

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

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

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 $\displaystyle (1,1)$