Question

Solve the linear system by graphing.

$\begin{array}{l}x+y=6\\ 2x-8y=-11\end{array}$

Short answer

Solution of the given system is $\left(3.7,2.3\right)$.

Step-by-step solution

Step 1. Given Information.

Linear system is:

$\begin{array}{l}x+y=6\\ 2x-8y=-11\end{array}$

Step 2. Property used.

Substitution property.

Step 3. Calculation.

For equation: $x+y=6$

Put the value of x in y, Hence,

For equation: $2x-8y=-11$

Put the value of x in y, Hence,

Now, both lines meet at point$\left(3.7,2.3\right)$.

Equation 1: $x+y=6$

Equation 2: $2x-8y=-11$

By substituting the value of y from equation 1 to equation 2.

$\begin{array}{c}2x-8\left(6-x\right)=-11\\ 2x-48+8x=-11\\ 10x=-11+48\\ x=\frac{37}{10}\end{array}$

Now substituting the value of x in equation 1.

$\begin{array}{c}\frac{37}{10}+y=6\\ y=6-\frac{37}{10}\\ =\frac{23}{10}\end{array}$

Hence, both lines meet at point$\left(3.7,2.3\right)$.

Step 4. Conclusion.

The solution to the given linear system is$\left(3.7,2.3\right)$.