Q 332 - Intermediate Algebra

Question

In the following exercises, solve the following system of equations by graphing 

$$\begin{gathered} 2x-y=5 \\ 4x-2y=10 \end{gathered}$$

Step-by-Step Solution

Answer

The solution to the linear equations infinitely many.

Step 1. Given information

The given equations are

$$\begin{gathered} 2x-y=5 \\ 4x-2y=10 \end{gathered}$$

Step 2. Finding intersecting points

First, solve both of these equations for y such that their slopes and y intercepts may be easily graphed.

And find the slope and y-intercept by solving the first equation for y.

$$\begin{gathered} 2x-y=5 \\ -y=-2x+5 \\ y=2x-5 \\ \mathrm{Here} \mathrm{the} \mathrm{slope} \mathrm{is} \mathrm{m}=2 \\ \mathrm{And} \mathrm{the} \mathrm{y}-\mathrm{intercept} is b=-5 \\ \mathrm{Again} \mathrm{Solve} \mathrm{the} \mathrm{second} \mathrm{equation} \mathrm{for} \mathrm{y}. \\ \mathrm{and} \mathrm{find} \mathrm{the} \mathrm{slope} \mathrm{and} \mathrm{y}-\mathrm{intercept}. \\ 4x - 2y = 10 \\ - 2y = - 4x + 10 \\ y = 2x - 5 \\ \mathrm{Here} \mathrm{the} \mathrm{slope} \mathrm{is} \mathrm{m} = 2 \\ \mathrm{And} \mathrm{the} \mathrm{y}-\mathrm{intercept} \mathrm{is} b = - 5 \end{gathered}$$

Step 3. Graph obtained

The lines are identical.

There are an endless number of ordered pairs that make both equations true because every point on the line does.

As a result, this system has an endless number of solutions.