Q11. - Algebra 1

Question

Use substitution to solve each system of equations.  

$\begin{array}{c}x+y=6\\ x-y=8\end{array}$

Step-by-Step Solution

Answer

The required solution is represented by $x=7$ and $y=-1$.

Step 1. Number the provided equations.

Make consideration that,

$\begin{array}{l}x+y=6\mathrm{......}\left(1\right)\\ x-y=8\mathrm{......}\left(2\right)\end{array}$

Step 2. Take the help of equation (2) to get the value of x after it use the obtained value to get the value of y .

Perform addition of y on both sides of the equation (2) to get the value of x in the form of an expression.

$x=8+y\mathrm{......}\left(3\right)$

Use the obtained value of x for the equation (1) to extract the value of y. 

$$\begin{gathered} 8+y+y=6 \\ 2y=6-8 \\ 2y=-2 \\ y=\frac{-2}{2} \\ =-1 \end{gathered}$$

Use the obtained value of y into equation (3) to get the value of x.

$$\begin{gathered} x=8-1 \\ =7 \end{gathered}$$

Step 3. Write the conclusion.

The obtained value of x and y represents the required solution that is $x=7$ and $y=-1$.