Chapter 3.1, Problem 26PPS

To determine

To solve: the system of equations $y=5x+3$ and $y=x-9$ by using a table.

Answer to Problem 26PPS

  $\left(x,y\right)=\left(-3,-12\right)$

Explanation of Solution

Given:

The system of equations:

  $\begin{array}{c}y=5x+3\\ y=x-9\end{array}$

To solve the given system of equation, substitute different values of x till the corresponding y -values of both the lines are same.

x	$y=5x+3$	$y=x-9$
0	$y=5\left(0\right)+3=3$	$y=0-9=-9$
1	$y=5\left(1\right)+3=8$	$y=1-9=-8$
$-1$	$y=5\left(-1\right)+3=-2$	$y=-1-9=-10$
2	$y=5\left(2\right)+3=13$	$y=2-9=-7$
$-2$	$y=5\left(-2\right)+3=-7$	$y=-2-9=-11$
3	$y=5\left(3\right)+3=18$	$y=3-9=-6$
$-3$	$y=5\left(-3\right)+3=-12$	$y=3-9=-12$

The corresponding y -values of both the lines are same when $x=-3$ .

So, solution of the given system of equations is $\left(x,y\right)=\left(-3,-12\right)$ .