Question

In the following exercises, solve the systems of equations by elimination.

$\left\{\begin{array}{l}x+y=12\\ x-y=-10\end{array}\right.$

Short answer

The solution for the system of linear equation is$\left(1,11\right)$.

Step-by-step solution

Step 1. Given information.

The system of linear equations,

$\left\{\begin{array}{l}x+y=12\\ x-y=-10\end{array}\right.$

Step 2. Calculating the value of y.

Now, on subtracting the equations we will eliminate $x$terms.

$x+y=12-x+y=+102y=22y=11$

Step 3. Calculating the value of x.

Substituting the value of $y$in any equation.

$$\begin{gathered} x+11=12 \\ x=1 \end{gathered}$$

Step 4. Checking the result.

Substituting the value of $x$and $y$in the first equation then

$$\begin{gathered} x+y=12 \\ 1+11=12 \\ 12=12 \end{gathered}$$

Substituting the value of $x$and $y$in the second equation then

$$\begin{gathered} x-y=-10 \\ 1-11=-10 \\ -10=-10 \end{gathered}$$

Hence, this is true.