Solve each system by elimination
x + 4y =6
3x + 12y = 18
x + 4y =6
3x + 12y = 18
Those two lines are the same
multiply the first one by 3 and you will see that.
They lie on top of each other so there is no single point of intersection, no unique solution.
To solve the system of equations by elimination, you can multiply one equation by a factor to make the coefficients of one of the variables in both equations cancel each other out.
Let's start by multiplying the first equation by -3:
-3(x + 4y) = -3(6)
-3x - 12y = -18
Now let's write down both equations together:
-3x - 12y = -18
3x + 12y = 18
Next, add the equations together to eliminate the y variable:
(-3x - 12y) + (3x + 12y) = -18 + 18
Simplifying this equation, we get:
0 = 0
Since 0 is always true, this means that the two equations are equivalent and have infinitely many solutions. The two equations represent the same line on the coordinate plane, so any point on that line will satisfy both equations.
Therefore, the system is consistent and dependent, and the solution set is all the points on the line x + 4y = 6.