Question

Pre algebra,solve system of equations by graphing need help on this

Answer 1

`(4,3)`

Step-by-step explanation

We want to solve the system of equations by graphing:

`\begin{gathered} y=x-1 \\ x+4y=16 \end{gathered}`

To do this, we have to plot the line graphs of both equations and then find the point where they intersect.

The point where the two lines intersect is the solution.

To plot the graphs of the equations, we need to find two points for each of the equations.

To do this, find the x and y intercepts i.e. the value of x when y = 0 and the value of y when x = 0.

For the first equation:

`\begin{gathered} \text{when y = 0:} \\ 0=x-1 \\ x=1 \\ \text{when x = 0:} \\ y=0-1 \\ y=-1 \end{gathered}`

So, we have two points (0, -1) and (1, 0)

For the second equation:

`\begin{gathered} \text{when y = 0:} \\ x+4(0)=16 \\ x=16 \\ \text{when x = 0:} \\ 0+4y=16\Rightarrow4y=16 \\ \Rightarrow y=(16)/(4) \\ y=4 \end{gathered}`

So, we have two points (0, 4) and (16, 0)

Now, plot the graph:

The lines intersect at (4, 3).

That is the solution of the system of equations.