Chapter 9, Problem 1RVS

Match each equation, inequality, or system of equations or inequalities with its graph.

$x-y=3,$

$2x+y=1$

To determine

The match of the graph of the system of equations $x-y=3$ and $2x+y=1$ from the provided graphs.

Answer to Problem 1RVS

Solution:

The correct match of the graph for the system of equations $x-y=3$ and $2x+y=1$ is option $\left(B\right)$, that is

Explanation of Solution

Given information:

The given system of equations is $x-y=3$ and $2x+y=1$.

The given options of graphs are:

And

The given equations can be plotted on the graph one by one by the following procedure:

Step 1. Considering an equation, first put $x=0$ and get the value of $y$ $\left(\text{say }{y}_1\right)$, then one point on the graph will be $\left(0,y_1\right)$.

Step 2. Now, put $y=0$ and get the value of $x$ $\left(\text{say }{x}_1\right)$, then another point on the graph will be $\left(x_1,0\right)$.

Step 3. Now, join the two points to get the line of the given equation.

For the first equation which is $x-y=3$.

Put $x=0$,

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

So, the first point will be $\left(0,-3\right)$.

For the second point, put $y=0$,

$\begin{array}{c}x-0=3\\ x=3\end{array}$

So, the second point will be $\left(3,0\right)$.

Therefore, the two points for the line $x-y=3$ are $\left(0,-3\right)\text{ and }\left(3,0\right)$.

Similarly, for the second line which is $2x+y=1$.

Put $x=0$,

$\begin{array}{c}2\left(0\right)+y=1\\ y=1\end{array}$

So, the first point will be $\left(0,1\right)$.

For the second point, put $y=0$,

$\begin{array}{c}2x+0=1\\ 2x=1\\ x=\frac{1}{2}\end{array}$

So, the second point will be $\left(\frac{1}{2},0\right)$.

Therefore, the two points for the line $2x+y=1$ are $\left(0,1\right)\text{ and }\left(\frac{1}{2},0\right)$.

The graph for the two equation of lines is given below:

Plot the points $\left(0,-3\right)\text{ and }\left(3,0\right)$ and join the points that gives the line $x-y=3$.

Again, plot the points $\left(0,1\right)\text{ and }\left(\frac{1}{2},0\right)$ and join the points that gives the line $2x+y=1$.

That is,

Therefore, the correct match for the graph of the equations $x-y=3$ and $2x+y=1$ is option (B).