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

Step 1: Understanding the Concept:
To solve a system of equations graphically, we plot both lines on the Cartesian plane. The point where the two lines intersect is the solution to the system.
Step 2: Detailed Explanation:
Plotting \(x = -3\):
This is a vertical line passing through the point \((-3, 0)\) on the x-axis.
Plotting \(5x - 2y = -5\):
Find at least two points for this line:
1. Let \(x = -1\): \(5(-1) - 2y = -5 \implies -5 - 2y = -5 \implies -2y = 0 \implies y = 0\). Point is \((-1, 0)\).
2. Let \(x = 1\): \(5(1) - 2y = -5 \implies 5 - 2y = -5 \implies -2y = -10 \implies y = 5\). Point is \((1, 5)\).
3. To find intersection with \(x = -3\), substitute \(x = -3\) into the second equation:
\(5(-3) - 2y = -5\)
\(-15 - 2y = -5\)
\(-2y = -5 + 15\)
\(-2y = 10 \implies y = -5\)
The line passes through \((-3, -5)\).
Graphing:
Draw the axes and plot the vertical line \(x = -3\).
Plot the points \((-1, 0), (1, 5)\), and \((-3, -5)\) and draw the line for \(5x - 2y = -5\).
The intersection point is clearly seen at \((-3, -5)\).
Step 3: Final Answer:
The solution to the system is \(x = -3\) and \(y = -5\).