Question

Use graphical method to solve the system of linear equations: x = –3 and 5x – 2y = –5.

Answer 1

1. Identify the equations

The given system consists of two linear equations:

x = –3   ...(Equation 1)

5x – 2y = –5   ...(Equation 2)

2. Table of values for equation 1 (x = –3)

This is a vertical line where x is always –3, regardless of the value of y.

x	y	Point
–3	0	(–3, 0)
–3	–5	(–3, –5)

3. Table of values for equation 2 (5x – 2y = –5)

Rearrange the equation to isolate y:

2y = 5x + 5

⇒ y = 2.5x + 2.5

Now, find a few points to plot the line:

If x = –1:

y = 2.5(–1) + 2.5

= 0

⇒ Point: (–1, 0)

If x = –3:

y = 2.5(–3) + 2.5

= –7.5 + 2.5

= –5

⇒ Point: (–3, –5)

4. Graphical representation

Plotting both lines on a coordinate plane:

The line x = –3 is a vertical line passing through x = –3.

The line 5x – 2y = –5 passes through points like (–1, 0) and (–3, –5).

5. Find the point of intersection

The two lines intersect at the point (–3, –5). This point satisfies both equations simultaneously.

The solution to the system of linear equations is x = –3 and y = –5.