# How do you solve the system 3x-2y=6 and x+y=2 by graphing?

Jan 1, 2016

the solution is (2 , 0)

#### Explanation:

these are linear equations ie. straight lines.
when these lines intersect with the y-axis then x-coordinate = 0
let x = 0 in 3x - 2y = 6 → 0 - 2y = 6 → y = -3 hence point ( 0 , -3 )
when these lines intersect with the x-axis then y-coordinate = 0
let y = 0 in 3x - 2y = 6 → 3x - 0 = 6 → x = 2 hence point ( 2 , 0 )
plot ( 0 , -3 ) and ( 2 , 0) on squared paper and you have the line with equation 3x - 2y = 6
Similarly for x + y =2
let x = 0 →y = 2 hence point (0 , 2 )
let y = 0 → x = 2 hence point 2 , 0 )
now plot ( 0 , 2 ) and (2 , 0 ) on the same graph as 3x - 2y = 6 and where the 2 lines intersect is the solution to the system of equations.