Questions: Solve the system below with the graphing method. Submit your answer as an ordered pair (x, y) without spaces. If there is more than one solution, enter (x, mx-b) where m and b are integers. If there is no solution, write: No Solution 5x-y=10 -15x+3y=-30

Solve the system below with the graphing method. Submit your answer as an ordered pair (x, y) without spaces. If there is more than one solution, enter (x, mx-b) where m and b are integers. If there is no solution, write: No Solution 5x-y=10 -15x+3y=-30
Transcript text: Solve the system below with the graphing method. Submit your answer as an ordered pair ( $x, y$ ) without spaces. If there is more than one solution, enter ( $x, m x-b$ ) where $m$ and $b$ are integers. If there is no solution, write: No Solution \[ \begin{array}{c} 5 x-y=10 \\ -15 x+3 y=-30 \end{array} \]
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Solution

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Solution Steps

To solve the system of equations using the graphing method, we need to:

  1. Convert each equation to the slope-intercept form \( y = mx + b \).
  2. Plot both lines on a graph.
  3. Identify the point of intersection, which will be the solution to the system.
Step 1: Rewrite the Equations in Slope-Intercept Form

First, we need to rewrite each equation in the slope-intercept form \( y = mx + b \).

For the first equation: \[ 5x - y = 10 \] Solve for \( y \): \[ y = 5x - 10 \]

For the second equation: \[ -15x + 3y = -30 \] Divide the entire equation by 3 to simplify: \[ -5x + y = -10 \] Solve for \( y \): \[ y = 5x - 10 \]

Step 2: Analyze the Equations

We now have the following two equations in slope-intercept form: \[ y = 5x - 10 \] \[ y = 5x - 10 \]

Step 3: Determine the Relationship Between the Lines

Since both equations are identical, they represent the same line. This means that every point on the line \( y = 5x - 10 \) is a solution to the system.

Final Answer

Since the two lines are identical, there are infinitely many solutions. The solution can be represented as: \[ (x, 5x - 10) \]

\[ \boxed{(x, 5x-10)} \]

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