Question

Use graphical method to solve the system of linear equations : \(x = -3\) and \(5x - 2y = -5\).

Hint:

When one equation is of the form \(x = c\), you already know the x-coordinate of the solution. Simply find the corresponding y-value in the second equation to verify your graph.

Answer 1

We need to solve graphically the system:
1) \( x = -3 \)
2) \( 5x - 2y = -5 \)

Step 1: Draw the line \( x = -3 \)
This is a vertical line passing through all points whose x–coordinate is –3.
Example points:
(–3, 0), (–3, 2), (–3, –2)

Step 2: Draw the line \( 5x - 2y = -5 \)
Convert to slope form:
\[ -2y = -5 - 5x \] \[ y = \frac{5 + 5x}{2} \]
Choose any two points:
• If \(x = 0\): \[ y = \frac{5}{2} = 2.5 \] So point (0, 2.5)

• If \(x = -3\): \[ y = \frac{5 + 5(-3)}{2} = \frac{5 - 15}{2} = \frac{-10}{2} = -5 \] So point (–3, –5)

Step 3: Plot both lines on the graph
• Draw vertical line x = –3.
• Draw slanted line through (0, 2.5) and (–3, –5).

Point of intersection:
The two lines meet at the point (–3, –5).

Step 4: Verify
Put \( x = -3 \) in second equation:
\[ 5(-3) - 2y = -5 \] \[ -15 - 2y = -5 \] \[ -2y = 10 \] \[ y = -5 \] Matches the graphical result.

Final Answer:
The solution of the system is: \[ \boxed{(-3,\ -5)} \]