To solve these simultaneous equations graphically, we need to find the point where the two lines intersect. The coordinates of this intersection point (x, y) are the solution to the system of equations.
Let's go through each graph one by one:
1.
First Graph:
- Equations: \( y = 2x + 1 \) and \( y = 4x - 3 \)
- Intersection point: The lines cross at \( x = 2 \) and \( y = 5 \).
- Solution: \( (2, 5) \)
2.
Second Graph:
- Equations: \( y = x - 5 \) and \( y = -2x + 4 \)
- Intersection point: The lines cross at \( x = 3 \) and \( y = -2 \).
- Solution: \( (3, -2) \)
3.
Third Graph:
- Equations: \( y = 3x + 5 \) and \( y = -x - 3 \)
- Intersection point: The lines cross at \( x = -2 \) and \( y = -1 \).
- Solution: \( (-2, -1) \)
4.
Fourth Graph:
- Equations: \( y = 5x + 1 \) and \( y = 3x + 2 \)
- Intersection point: The lines cross at \( x = -0.5 \) and \( y = -1.5 \).
- Solution: \( (-0.5, -1.5) \)
5.
Fifth Graph:
- Equations: \( y = 2x - 4 \) and \( y = -3x + 1 \)
- Intersection point: The lines cross at \( x = 1 \) and \( y = -2 \).
- Solution: \( (1, -2) \)
6.
Sixth Graph:
- Equations: \( y = 4x + 2 \) and \( y = 5 - 2x \)
- Intersection point: The lines cross at \( x = 0.5 \) and \( y = 4 \).
- Solution: \( (0.5, 4) \)
Final Answer:
(2, 5), (3, -2), (-2, -1), (-0.5, -1.5), (1, -2), (0.5, 4)
Parent Tip: Review the logic above to help your child master the concept of worksheet solving systems of equations by graphing.
