Chapter 3.1, Problem 7CYU

To determine

To solve: the system of equations $4x+5y=-41$ and $3y-5x=5$ by using graph.

Answer to Problem 7CYU

  $\left(x,y\right)=\left(-4,-5\right)$

Explanation of Solution

Given:

The system of equations:

  $\begin{array}{c}4x+5y=-41\\ 3y-5x=5\end{array}$

The solution of the given system of equation is the point of intersection of the lines given by these two equations.

Now, to graph $4x+5y=-41$

First substitute $x=0$ in the above equation,

  $\begin{array}{c}4\left(0\right)+5y=-41\\ 0+5y=-41\\ 5y=-41\\ y=-8.2\end{array}$

Now substitute $y=0$ in the above equation,

  $\begin{array}{c}4x+5\left(0\right)=-41\\ 4x+0=-41\\ 4x=-41\\ x=-10.25\end{array}$

Now plot the points $\left(0,-8.2\right)$ and $\left(-10.25,0\right)$ and draw a line passing through these points. This line is the graph of the equation $4x+5y=-41$ .

Now, to graph $3y-5x=5$

First substitute $x=0$ in the above equation,

  $\begin{array}{c}3y-5\left(0\right)=5\\ 3y-0=5\\ 3y=5\\ y=1.667\end{array}$

Now substitute $y=0$ in the above equation,

  $\begin{array}{c}3\left(0\right)-5x=5\\ 0-5x=5\\ -5x=5\\ x=-1\end{array}$

Now plot the points $\left(0,1.667\right)$ and $\left(-1,0\right)$ and draw a line passing through these points. This line is the graph of the equation $3y-5x=5$ .

The required graph is:

  

The point of intersection of the two lines is $\left(-4,-5\right)$ .

So, solution of the given system of equations is $\left(x,y\right)=\left(-4,-5\right)$ .