Questions: Graph the system of equations, and determine the x+5 y = 5 2 x+10 y = 50

Transcript text: Graph the system of equations, and determine th \[ \begin{aligned} x+5 y & =5 \\ 2 x+10 y & =50 \end{aligned} \]

Solution

Solution Steps

Step 1: Solve the system of equations

We start by solving the system of linear equations: \[ \begin{aligned} x + 5y &= 5 \\ 2x + 10y &= 50 \end{aligned} \]

Step 2: Simplify the second equation

Notice that the second equation can be simplified by dividing all terms by 2: \[ x + 5y = 25 \]

Step 3: Compare the equations

Now we have: \[ \begin{aligned} x + 5y &= 5 \\ x + 5y &= 25 \end{aligned} \]

Step 4: Determine the consistency

Since the left-hand sides of the equations are identical but the right-hand sides are different, the system of equations is inconsistent and has no solution.

Final Answer

The system of equations has no solution.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = (1/5)(5 - x)", "y = (1/5)(25 - x)"], "latex_expressions": ["$x + 5y = 5$", "$x + 5y = 25$"]}

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Next >

Thank you for your feedback.

Copied!