Chapter 4, Problem 1RP

To determine

The point of intersection by graphing the lines.

Answer to Problem 1RP

Solution: The point of intersection for equations is $\left(-3,2\right)$.

Explanation of Solution

Given: The equations are,

$2x+3y=0$

$-x+3y=9$

Calculation: The equations are,

$2x+3y=0$ …… (1).

$-x+3y=9$ …… (2).

Draw the graph for both equations. by finding $x$ intercept and $y$ intercept for equation (1) and equation (2).

Calculate the values for $x$ and $y$ from equation (1).

Substitute $0$ for $x$ in equation (1) to get y intercept.

$\begin{array}{c}2\left(0\right)+3y=0\\ 0+3y=0\\ y=0\end{array}$

The value obtained for $y=0$.

Substitute $-2$ for $y$ in equation (1).

$\begin{array}{c}2x+3\left(-2\right)=0\\ 2x-6=0\\ 2x=6\\ x=3\end{array}$

The value obtained for $x$ is 3.

Draw a line passing through the point $\left(0,0\right)$ and $\left(3,-2\right)$.

Calculate the values for $x$ and $y$ from equation (1)

Substitute $0$ for $x$ in equation (2) to get y intercept.

$\begin{array}{c}-0+3y=9\\ 3y=9\\ y=3\end{array}$

The value obtained for $y$ is $3$

Substitute 0 for $y$ in equation (2) to get $x$ intercept.

$\begin{array}{c}-x+3\left(0\right)=9\\ x=-9\end{array}$

The value obtained for $x$ is $-9$

Draw a line passing through the point $\left(0,3\right)$ and $\left(-9,0\right)$.

Figure (1)

Figure (1) shows the graph for both equations in which a point $\left(-3,2\right)$ is the point of intersection.

Conclusion:

Therefore, the intersection point of given equations is $\left(-3,2\right)$.