Questions and Answers
What is the solution to the system of linear equations: -1/2y=1/2x+5 and y=2x+2?
(-4, -6)
What is the solution of the system of linear equations: 3y = 3/2x + 6 and 1/2y - 1/4x = 3?
No solution
What is the solution to the system of linear equations: 2x + 3y = 16.9 and 5x = y + 7.4?
(2.3, 4.1)
Approximately how many weeks will it take for both plants to reach the same height given the equations of Plant A: y = 1.8x + 3.1 and Plant B: y = 2.3x + 1.9?
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What is the solution to the system of linear equations after graphing: y + 2.3 = 0.45x and -2y = 4.2x - 7.8?
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For what value of b will the equations 3y + 12 = 6x and 2y = 4x + b form a system of linear equations with infinitely many solutions?
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Why would someone choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand?
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Study Notes
Systems of Linear Equations: Graphing Solutions
- Graphing the equations -1/2y = 1/2x + 5 and y = 2x + 2 gives a solution of (-4, -6).
- The system 2y = x + 10 and 3y = 3x + 15 has one solution, with both equations sharing the same y-intercept.
- The system 3y = 3/2x + 6 and 1/2y - 1/4x = 3 results in no solution.
- The solution to the equations 2x + 3y = 16.9 and 5x = y + 7.4 is approximately (2.3, 4.1) rounded to the nearest tenth.
- Plant growth equations: Plant A: y = 1.8x + 3.1 and Plant B: y = 2.3x + 1.9 intersect at about 2.4 weeks.
- For the system involving 3y + 12 = 6x and 2y = 4x + b to have infinitely many solutions, b must equal -8.
Advantages of Using Graphing Calculators
- Graphing calculators provide more accurate results than hand-drawn graphs, especially with fractional or decimal slopes and y-intercepts.
- They increase efficiency by accepting various forms of linear equations and allowing quick adjustments to graph settings without redrawing.
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Description
This quiz covers the concepts of graphing systems of linear equations. It includes solving equations and interpreting their intersections in graphical form. Master the techniques required to find solutions and understand the relationships between different linear equations.
