Question

Solve each system by graphing. Check your answer. Y=x-22x+y=1

Answer 1

We have the equations :

`\begin{gathered} y\text{ = x - 2} \\ 2x\text{ + y = 1} \end{gathered}`

To solve graphically, we should plot the graph of the equation on the same graph.

For y = x-2

We can obtain two points to plot the graph of y = x-2

At x= 0:

`\begin{gathered} y\text{ = 0-2} \\ =\text{ -2} \end{gathered}`

At y= 0:

`\begin{gathered} 0=\text{ x-2} \\ x\text{ = 2} \end{gathered}`

We have the points : (0,-2) and (2,0)

For 2x + y =1

At x = 0:

`\begin{gathered} 0\text{ + y = 1} \\ y\text{ =1} \end{gathered}`

At y = 0:

`\begin{gathered} 2x\text{ + 0 = 1} \\ x\text{ = }(1)/(2) \end{gathered}`

We have the points : (0, 1) and (1/2, 0)

Plotting these points gives the graph shown below:

From the graph, we have the point of intersection of the two lines as (1,-1)

Hence, the solution to the system of equation is (1, -1)