# How do you solve the system of linear equations #x + 3y = 9# and #2x + 6y = 12#?

##### 2 Answers

There is no solution.

#### Explanation:

Doubling the first equation

But this is inconsistent with the second equation

Hence, there is no solution.

Drawing graphically these represent two different but parallel lines, who do not intersect and hence there is no solution.

graph{(x+3y-9)(2x+6y-12)=0 [-2.92, 7.08, -0.42, 4.58]}

Follow the method

#### Explanation:

x + 3y = 9

2x + 6y = 12

First you check if the two equations are compatible, that is

if they are parallel, they must not intersect.

Parallel means they have the same slope, given by dy/dx in general, and in the case of linear equations by the ratio of the y coefficient to that of x, that is 3 for the first equation, and 3 for the second. Since these two equations are parallel, they are multiple of each other. Now where these straight lines intersect the axis y = 0, that is the x-axis, is the constant term on the right hand side. Try it

Put y = 0 you get x = 9, for the first equation, and y = 0, x = 6 for the second equation, This is geometrically impossible, and therefore algebraically too. So this problem has no solution.