Question

Solve this problem using elimination.
1/3x + 1/2y = 0
1/2x + 1/5y = 11/5

Answer 1

Fractions are a little tricky, but once you get used to them, they are like any number, so let's see:
\[\frac{ 1 }{ 3 }x+\frac{ 1 }{ 2 }y=0\]
\[\frac{ 1 }{ 2 }x+\frac{ 1 }{ 5 }y=\frac{ 11 }{ 5 }\]
Let's make the variables opposite in this problem, and use elimination,
let's begin by multiplying the first equation by -6 and the second by 4, operate and order up:
\[-2x-3y=0\]
\[2x+\frac{ 4 }{ 5 }y=\frac{ 44 }{ 5 }\]
So, sum up both equations, to get rid of the x term and associating the y terms we get:
\[(\frac{ 4 }{ 5 }-3)y=\frac{ 44 }{ 5 }\]
Solving the operation on the inside of the parenthessis:
\[(\frac{ 4-15 }{ 5 })y=\frac{ 44 }{ 5 }\]
operating a little and reordering:
\[-11y=44\]
And we have found that y=(-4)
Let's take the initial equation (any of them) and replace and find the x value:
\[\frac{ 1 }{ 3 }x+\frac{ 1 }{ 2 }(-4)=0\]
multiplying and ordering up, also adding 2 on both sides:
\[\frac{ 1 }{ 3 }x=2\]
solving for x we get that x=6, so we conclude that the solution is:
\[x=6\]
\[y=-4\]