Question

Solve the following system of equations graphically:

3x + y + 4 = 0

3x – y + 2 = 0

Answer 1

Step 1: Find points for the first line 3x + y + 4 = 0

We can express y in terms of x:

y =  –3x – 4

Let’s choose two convenient values for x to find their corresponding y-values:

If x = 0: y = –3(0) – 4 = – 4

⇒ (0, – 4)

If x = –1: y = –3(–1) – 4 = 3 – 4

⇒ (–1, –1)

x	y	Point
0	– 4	(0, – 4)
–1	–1	(–1. –1)

Step 2: Find points for the second line 3x – y + 2 = 0

We can express y in terms of x:

y = 3x + 2

If x = 0: y = 3(0) + 2 = 2

⇒ (0, 2)

If x = –1: y = 3(–1) + 2 = –3 + 2 = –1

⇒ (–1, –1)

x	y	Point
0	2	(0, 2)
–1	–1	(–1. –1)

Step 3: Graphical visualization

Plotting both lines on the Cartesian plane allows us to observe where they intersect: 

Final verification

Both lines clearly intersect at the point (–1, –1). We can verify this algebraically by substituting the values into the original equations:

1. First equation:

3(–1) + (–1) + 4

= –3 – 1 + 4 

= 0 (True)

2. Second equation:

3(–1) – (–1) + 2

= –3 + 1 + 2

= 0 (True)

Thus, the graphical solution is uniquely verified at x = –1 and y = –1.