# Solve this system of equations: 4x-2y=6, 3x+y=2?

Nov 11, 2017

See below

#### Explanation:

Assuming second equation is $4 x - 2 y = 6$
Using substitution:

Isolate $y$ in first equation:
$3 x + y = 2$
$y = 2 - 3 x$

Sub $y = 2 - 3 x$ into second equation:
$4 x - 2 \left(2 - 3 x\right) = 6$
$4 x - 4 + 6 x = 6$
$10 x - 4 = 6$
$10 x = 6 + 4$
$10 x = 10$
$x = 1$

Sub $x = 1$ into first equation:
$3 \left(1\right) + y = 2$
$3 + y = 2$
$y = 2 - 3$
$y = - 1$
$\therefore P O I = \left(1 , - 1\right)$

Alternatively, graph both lines to find the point of intersection.

Here's the graph:

#### Explanation:

graph{(3x+y-2)(4x-2y-6)=0}