Chapter 6.CT, Problem 1CT

To determine

To solve:

The system $\{\begin{array}{l}x-3y=-5\\ 2x-y=0\end{array}$ by graphing method.

Answer to Problem 1CT

Solution:

The required graph is,

The solution of the system of equations is given by $\left\{\left(x,y\right)=\left(1,2\right)\right\}.$

Explanation of Solution

Approach:

To solve a system of equations by graphing, graph each equation in the system and find the coordinates of the point where all of the graphs intersect.

If the graphs have no point in common, the system has no solutions. If the graphs coincide, the system has infinitely many solutions.

Calculation:

Given,

$\{\begin{array}{l}x-3y=-5\\ 2x-y=0\end{array}$

The graphs of the equations are the lines are given by,

From the graph,

The co-ordinates of point where the graphs intersect is $\left(1,2\right).$

Thus, the solution of equations is $\left(1,2\right).$

Final statement:

Therefore, the solution of the system of equations is given by $\left\{\left(x,y\right)=\left(1,2\right)\right\}.$