Chapter 10, Problem 1RE

To determine

The solution of the system of equations $y=5x-1$ and $y=3x+3$ by graphing.

Answer to Problem 1RE

The solution of the system of equations $y=5x-1$ and $y=3x+3$ is $\underset{\_}{x=2\text{and }y=9}$.

Explanation of Solution

Given:

The system of equations are $y=5x-1$ and $y=3x+3$.

Procedure used:

To solve a system of two equations on the same pair of axes:

1. Graph each equation on the same pair of axes.

2. The solution will be the common point.

Calculation:

Obtain the solution of the system of equations $y=5x-1$ and $y=3x+3$ by graphing as follows.

Assume values for the variable x and obtain the values for the variable y for the equation $y=5x-1$ as shown in the below Table 1.

x	$y=5x-1$	$\left(x,y\right)$
2	9	$\left(2,9\right)$
1	4	$\left(1,4\right)$
0	–1	$\left(0,-1\right)$

Table 1

Similarly, assume values for the variable x and obtain the values for the variable y for the equation $y=3x+3$ as shown in the below Table 2.

x	$y=3x+3$	$\left(x,y\right)$
2	9	$\left(2,9\right)$
1	6	$\left(1,6\right)$
0	3	$\left(0,3\right)$

Table 2

Graph each equation on the same set of axes by the use of the co-ordinate values from Table 1 and Table 2 as shown in the below figure.

From Figure 1, it is observed that the two graphs intersect at $\left(2,9\right)$.

Thus, the solution of the system of equations is $\underset{\_}{x=2\text{and }y=9}$.

Check whether the solution is correct by substituting the solution $\left(2,9\right)$ in the equation $y=5x-1$ as,

$\begin{array}{l}y=5x-1\\ 9\stackrel{?}{=}5\left(2\right)-1\\ 9\stackrel{?}{=}10-1\\ 9=9\end{array}$

Thus, the solution $\left(2,9\right)$ satisfies the equation $y=5x-1$.

Similarly, substitute the solution $\left(2,9\right)$ in the original equation $y=3x+3$ as,

$\begin{array}{l}y=3x+3\\ 9\stackrel{?}{=}3\left(2\right)+3\\ 9\stackrel{?}{=}6+3\\ 9=9\end{array}$

Thus, the solution $\left(2,9\right)$ satisfies the equation $y=3x+3$.