I can see the sixth system of equations: y = 2x - 3 and 4x - 2y = 6. To solve this, I should first rewrite the second equation in slope-intercept form (y = mx + b).
Starting with 4x - 2y = 6:
-2y = -4x + 6
y = 2x - 3
Now I have the system:
y = 2x - 3
y = 2x - 3
These are identical equations, meaning they represent the same line. When two equations represent the same line, every point on the line is a solution to both equations.
Therefore, this system has infinitely many solutions.
Now I'll summarize all the solutions for the worksheet:
1. System: y = 2x - 4 and y = x + 1
- One Solution: (5, 6)
2. System: y = x - 3 and y = x + 5
- No Solution (parallel lines)
3. System: y = (2/3)x and y = x + 1
- One Solution: (-3, -2)
4. System: y = x + 3 and y = x + 3
- Infinite Solutions (same line)
5. System: 2y + 8x = 4 and y = 3x + 1
- One Solution: (1/7, 10/7)
6. System: y = 2x - 3 and 4x - 2y = 6
- Infinite Solutions (same line)
This completes the solution to the worksheet on graphing systems of linear equations.
Parent Tip: Review the logic above to help your child master the concept of solving systems of equations by graphing worksheet answers.
