Questions: Solve the system of equations by graphing. 5x + 3y = 18 x + 3y = -6

Solve the system of equations by graphing. 5x + 3y = 18 x + 3y = -6
Transcript text: Solve the system of equations by graphing. \[ \left\{\begin{array}{l} 5 x+3 y=18 \\ x+3 y=-6 \end{array}\right. \]
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Solution

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Solution Steps

Step 1: Convert to slope-intercept form

The equations are converted to slope-intercept form:

  • Equation 1: \(y = -1.6666666666666667x + 6\)
  • Equation 2: \(y = -0.3333333333333333x - 2\)
Step 2: Find the point of intersection

The lines intersect at one point: \((x, y) = (6, -4)\).

Step 3: Verify the solution

The solution satisfies both original equations.

Final Answer:

The system of equations has a unique solution at \((x, y) = (6, -4)\).

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