Questions and Answers
What is the solution to the system of equations $y = 1.5x - 4$ and $y = -x$?
(1.6, -1.6)
Which value, when placed in the box, would result in a system of equations with infinitely many solutions for $y = 2x - 5$ and $2y - 4x = []$?
-10
How many minutes does it take Arnob to catch up to Kathleen when she has a 5-mile head start?
75
What is the solution to the system of equations represented by two tables?
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What does the solution of the system $x + y = 24$ and $3x + 5y = 100$ indicate about the questions on the test?
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What is the solution to the system of equations $y = -5 + 30$ and $x = 10$?
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In which step did Ernesto make the first error while solving his system of equations?
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What is the solution to the system of equations $y = rac{1}{2}x - 6$ and $x = -4$?
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What is the solution to the system of equations $y= rac{2}{3}x + 3$ and $x = -2$?
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What is the solution to the system of equations $y = 4x - 10$ and $y = 2$?
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What is the solution to the system of equations $y = -3x + 6$ and $y = 9$?
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What can Lian conclude from her result of $75=75$ after solving the system of linear equations for two gyms?
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What is the solution to the system of equations $y = -3x - 2$ and $5x + 2y = 15$?
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Which values, when placed in the box, would result in a system of equations with no solution? Check all that apply.
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What is the solution to the system of equations with the two linear equations shown?
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What is the solution to the system of equations $y = -5x + 3$ and $y = 1$?
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What is the solution to the system of equations $y = -3x - 2$ and $5x + 2y = 15$?
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What can Casey conclude from his result of $5=20$ after solving the system of linear equations?
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Study Notes
System of Equations Solutions
- Solution to the system: ( y = 1.5x - 4 ) and ( y = -x ) is ( (1.6, -1.6) ).
- Infinite solutions occur when ( 2y - 4x = -10 ) in the system ( y = 2x - 5 ).
- Arnob catches up to Kathleen in 75 minutes while running along a loop with a 5-mile head start.
Example Solutions
- The solution for the tables representing two linear functions is ( (8, -22) ).
- Science test consists of 10 three-point questions and 14 five-point questions reflecting the system ( x + y = 24 ) and ( 3x + 5y = 100 ).
- For the equations ( y = -5 + 30 ) and ( x = 10 ), the solution is ( (10, -20) ).
Error Identification
- Ernesto's first error in solving the system ( x - y = 7 ) and ( 3x - 2y = 8 ) occurs in Step 3.
Additional Solutions
- The solution to the equations ( y = \frac{1}{2}x - 6 ) and ( x = -4 ) is ( (-4, -8) ).
- For the system ( y = \frac{2}{3}x + 3 ) and ( x = -2 ), the solution is ( (-2, \frac{5}{3}) ).
- The solution for the equations ( y = 4x - 10 ) and ( y = 2 ) is ( (3, 2) ).
- For ( y = -3x + 6 ) and ( y = 9 ), the solution is ( (-1, 9) ).
Cost Comparison Conclusions
- Lian concludes both gyms charge the same monthly rate and membership fee after finding ( 75 = 75 ).
- Casey concludes that both landscapers charge the same hourly rate, but different fees per job after getting ( 5 = 20 ).
Identifying No Solution Scenarios
- Values leading to no solutions for ( y = -2x + 4 ) and ( 6x + 3y = [] ) include -12, -4, 0, and 4.
Final Solutions
- The solution to the system ( y = -3x - 2 ) and ( 5x + 2y = 15 ) is ( (-19, 55) ).
- A second identical solution for the equations ( y = -3x - 2 ) and ( 5x + 2y = 15 ) reinforces ( (-19, 55) ) as consistent.
Additional Linear System Solution
- The solution to the system of equations ( y = -5x + 3 ) and ( y = 1 ) is ( (0.4, 1) ).
- The solution to two linear equations in yet another unspecified system yields ( (7, \frac{13}{3}) ).
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Description
Test your knowledge on solving systems of linear equations using the substitution method. This quiz covers key concepts and problem-solving strategies vital for understanding linear algebra. Challenge yourself with practical problems and improve your skills!
