Answer:
The system of equations that describes the graph is:
x + y = 3
2x + 2y = 1
Step-by-step explanation:
Parallel lines have:
- Same slopes
- Different y-intercepts
- The system of equations which represent them is y = m x + b and y = m x + c, where b and c are the y-intercepts
Let us find the equation of each line
∵ The solid line passes through points (3 , 0) and (0 , 3)
∵ m = Δy/Δx
∴ Δy/Δx = [tex]\frac{3-0}{0-3}=\frac{3}{-3}[/tex]
∴ m = -1
∵ b is the y-intercept (value y at x = 0)
∵ y = 3 at x = 0
∴ b = 3
∴ y = - x + 3
- Add x to both sides
∴ x + y = 3 ⇒ (1)
∵ The dashed line passes through points (0.5 , 0) and (0 , 0.5)
∵ m = Δy/Δx
∴ Δy/Δx = [tex]\frac{0.5-0}{0-0.5}=\frac{0.5}{-0.5}[/tex]
∴ m = -1
∵ b is the y-intercept (value y at x = 0)
∵ y = 0.5 at x = 0
∴ b = 0.5
∴ The equation of the line is y = - x + 0.5
- Add x to both sides
∴ x + y = 0.5
- Multiply both sides by 2
∴ 2x + 2y = 1 ⇒ (2)
The system of equations that describes the graph is:
x + y = 3
2x + 2y = 1
