Q. 342 - Intermediate Algebra

Question

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

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

Step-by-Step Solution

Answer

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

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.