Solving linear systems using the elimination method is also known as using the addition/subtraction method. The goal is to "eliminate" one of the variables in order to solve the system of equations.
Simplifying we get:
Now let's look at the first equation. Multiply each term in the equation by 2.
`2 (x/2 +2y) = 2(27)`
`x+4y = 54`
Now let's go back to the second equation. Multiply each term in the equation by 3.
`3(x+ y/3) =3(10)`
Now the two equations will be easier to work with.
Let's eliminate the x variable to solve for y first. To do this multiply the first equation by -3.
`-3(x+4y=54)` >>> `-3x-12y=-162`
Now we have:
`3x +y =30`
The 3x and -3x cancel out. Combine -12y with 1y which is -11y. Finally -162 combined with 30 is -132.
`-11y = -132`
Divide both sides by -11 to get y alone.
Almost finished. Since you now know what y is, simply plug this value into one of the original equations to solve for x.
`1/2 x +2(12) =27`
`x/2 +24 =27`
`2 (x/2) = 2 (3)`
The solution to the system of equations is