To check if an ordered pair `(x,y)` is a solution of a linear equation, you need to plug-in the values of `x` and `y` on the equations, and check if results as a true statement.
For the first equation `-6x + y = -32,` replace `x` by `6` and replace `y` by `4` .
`-6(6)+4 ? -32`
`-36 + 4 ? -32`
`-32 = -32`
It is true that `-32` is equal to `-32` , so `(6,4)` lies on the line corresponds to`-6x+y=-32`.
For the second equation `x + y = 10` , replace x by `6` and replace y by `4` .
`6 + 4 ? 10`
`10 = 10`
It is true that `10 = 10` , therefore `(6,4)` lies on the line corresponds to `x + y = 10` .
Therefore `(6,4)` is a solution of the system.
To check the answer just input the values into any one of the linear equations,
-6x + y = -32
Let's see! In order to check if (6,4) you are going to have to plug in x as 6 and y as 4 into both equations and see if both sides are equal on both equations.