Question

Solve the linear system by graphing.

$\begin{array}{l}y=x-5\\ y=2x+1\end{array}$

Short answer

Solution of the given system is$\left(-6,-11\right)$.

Step-by-step solution

Step 1. Given Information.

Linear system is:

$\begin{array}{l}y=x-5\\ y=2x+1\end{array}$

Step 2. Property used.

Substitution property.

Step 3. Calculation.

For equation: $y=x-5$

Put the value of x in y, Hence,

For equation: $y=2x+1$

Put the value of x in y, Hence,

Now, both lines meet at point$\left(-6,-11\right)$.

Equation 1: $y=x-5$

Equation 2: $y=2x+1$

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

$\begin{array}{l}x-5=2x+1\\ x=-6\end{array}$

Now substituting the value of x in equation 1.

$\begin{array}{l}y=-6-5\\ =-11\end{array}$

Hence, both lines meet at point$\left(-6,-11\right)$.

Step 4. Conclusion.

The solution to the given linear system is$\left(-6,-11\right)$.