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Questions and Answers
What is the solution to the system of linear equations: -1/2y=1/2x+5 and y=2x+2?
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?
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?
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?
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?
What is the solution to the system of linear equations after graphing: y + 2.3 = 0.45x and -2y = 4.2x - 7.8?
What is the solution to the system of linear equations after graphing: y + 2.3 = 0.45x and -2y = 4.2x - 7.8?
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?
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?
Why would someone choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand?
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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