Question

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

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

Short answer

The solution to the linear equations infinitely many.

Step-by-step solution

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.

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

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.