Chapter 8.10, Problem 23HP

To determine

The system of equations and the slope intercept from when the solution of the system of eqns. is $\left(1,7\right)$ .

Answer to Problem 23HP

The system of equation is written as:

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

Explanation of Solution

Given:

The point of solution is $\left(1,7\right)$

Concept used:

The slope-intercept form is:

  $y=mx+b$

Where,

Slope: $m$

  $y-$ intercept: $b$

Calculation:

Know that:

  $y=mx+b$....... (1)

Put the value of points: $x=1,y=7$ in eq. (1)

  $7=1m+b$

  $m+b=7$....... (2) Consider, any two different two values of the $m$ in above eq. (2):

  $m+b=7$

Take value of $m=1$ then

  $\begin{array}{l}m+b=7\\ 1+b=7\\ b=6\end{array}$

Take value of $m=2$ then

  $\begin{array}{l}m+b=7\\ 2+b=7\\ b=5\end{array}$

So, new two equations are written as when $m=1,b=6$ and $m=2,b=7$

  $\begin{array}{l}y=1x+6,\\ y=x+6\end{array}$

And $y=2x+5$

Conclusion:

The system of equation is written as:

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