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Solving a system of equations by graphing on a homework sheet.

A hand using a red pen and ruler to solve a system of equations by graphing on a math worksheet.

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Show Answer Key & Explanations Step-by-step solution for: Homework #1 Unit 5 Lesson 1 (Algebra 1)

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1. Rewrite the equations in slope-intercept form (y = mx + b):
- x - y = 7 → y = x - 7
- x - y = -4 → y = x + 4

2. Graph both lines on the coordinate plane:
- For y = x - 7: The y-intercept is -7, and the slope is 1. Start at (0, -7) and use the slope to plot additional points.
- For y = x + 4: The y-intercept is 4, and the slope is 1. Start at (0, 4) and use the slope to plot additional points.

3. Identify the point of intersection:
- Since both lines have the same slope (1), they are parallel and will never intersect.

4. Conclusion:
- The system of equations has no solution because the lines are parallel and do not intersect.

Parent Tip: Review the logic above to help your child master the concept of system of linear equations and inequalities worksheet.

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