To check a solution for a without graphing, we need to substitute the solution into each equation. Then, we have to determine whether all of the equations in the system are true. Let's consider two examples.

### Example $1$

Suppose we are given a system and told the solution is

$(1,2).$
${x+y=33x−y=1 $
Let's check the given solution by substituting

$1$ and

$2$ for

$x$ and

$y,$ respectively.

${x+y=33x−y=1 (I)(II) $

${1+2=?33⋅1−2=?1 $

${1+2=?33−2=?1 $

${3=31=1 $

Since both equations are true,

$(1,2)$ is a solution to the system.

### Example $2$

Consider a second example now.

${2x+y=1x−2y=3 $
Suppose we are told

$(1,0)$ is a solution to the system. Let's see if that's correct!

${2x+y=1x−2y=3 (I)(II) $

${2⋅1+0=?11−2⋅0=?3 $

${2+0=?11−0=?3 $

${2 =11 =3 $

Since neither equation is true,

$(1,0)$ is not a correct solution to the system. Note that if only one of the equations produces a false statement, the solution is incorrect.