Questions and Answers
If 4x - y = 5 is one of the equations, which could be the other equation?
How many solutions does the linear system have for the equations y = 2x - 5 and -8x - 4y = -20?
one solution (2.5, 0)
What is the solution for the system of equations y = -1/2x + 4 and 2y = -8?
No solution
Muriel says she has written a system of two linear equations that has an infinite number of solutions. One of the equations is 3y = 2x - 9. Which could be the other equation?
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What is the solution to the system of equations 2x - y = 7 and y = 2x + 3?
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Which values of m and b will create a system of equations with no solution?
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What value of b will cause the system y = 6x + b and -3x + 1/2y = -3 to have an infinite number of solutions?
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What is the best approximation for the solution to the system y = -3 and y = x - 0.8?
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How many solutions does the linear system y = -6x + 2 and -12x - 2y = -4 have?
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Which equation could be Henry's if Fiona wrote the linear equation y = 2/5x - 5 and they discovered that his equation had all the same solutions?
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Study Notes
Systems of Linear Equations: Key Concepts
- A system of equations with one solution includes lines that intersect at a single point.
- Example equation indicating one solution: 4x - y = 5, with an alternative solution presented as y = -4x + 5.
Solutions to Linear Systems
- A given system with equations y = 2x - 5 and -8x - 4y = -20 has one solution at the point (2.5, 0).
- The equations y = -1/2x + 4 and 2y = -8 indicate no solution as the lines are parallel.
Infinite Solutions in Linear Systems
- Infinite solutions occur when two equations represent the same line.
- An equation that could yield infinite solutions: if 3y = 2x - 9, an alternative could be y = 2/3x - 3.
No Solutions in Linear Systems
- A system of equations such as 2x - y = 7 and y = 2x + 3 results in no solution as the lines overlap without intersecting.
- Values of m and b that produce no solution must result in parallel lines, exemplified by m = -2.
Special Cases in Systems of Equations
- For the equation y = 6x + b, choosing b = -6 leads to an infinite number of solutions when paired with another compatible equation.
- Graphing system: y = -3 and y = x - 0.8 produces a solution approximated at (-2.2, -3).
Relationships Between Equations
- The equations y = -6x + 2 and -12x - 2y = -4 will yield an infinite number of solutions, indicating they are equivalent.
- A line having all the same solutions as another can be represented in different forms, such as x - 2/5y = 25/2 being equivalent to y = 2/5x - 5.
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Description
Test your knowledge on solving systems of linear equations through graphing with this interactive quiz. Each question provides scenarios regarding possible solutions and the relationships between equations. See if you can identify the correct outcomes based on the equations provided!
