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Questions and Answers
What is the solution to the system of equations $y = 1.5x - 4$ and $y = -x$?
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 $2y - 4x = []$?
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?
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?
What is the solution to the system of equations represented by two tables?
What does the solution of the system $x + y = 24$ and $3x + 5y = 100$ indicate about the questions on the test?
What does the solution of the system $x + y = 24$ and $3x + 5y = 100$ indicate about the questions on the test?
What is the solution to the system of equations $y = -5 + 30$ and $x = 10$?
What is the solution to the system of equations $y = -5 + 30$ and $x = 10$?
In which step did Ernesto make the first error while solving his system of equations?
In which step did Ernesto make the first error while solving his system of equations?
What is the solution to the system of equations $y = rac{1}{2}x - 6$ and $x = -4$?
What is the solution to the system of equations $y = rac{1}{2}x - 6$ and $x = -4$?
What is the solution to the system of equations $y= rac{2}{3}x + 3$ and $x = -2$?
What is the solution to the system of equations $y= rac{2}{3}x + 3$ and $x = -2$?
What is the solution to the system of equations $y = 4x - 10$ and $y = 2$?
What is the solution to the system of equations $y = 4x - 10$ and $y = 2$?
What is the solution to the system of equations $y = -3x + 6$ and $y = 9$?
What is the solution to the system of equations $y = -3x + 6$ and $y = 9$?
What can Lian conclude from her result of $75=75$ after solving the system of linear equations for two gyms?
What can Lian conclude from her result of $75=75$ after solving the system of linear equations for two gyms?
What is the solution to the system of equations $y = -3x - 2$ and $5x + 2y = 15$?
What is the solution to the system of equations $y = -3x - 2$ and $5x + 2y = 15$?
Which values, when placed in the box, would result in a system of equations with no solution? Check all that apply.
Which values, when placed in the box, would result in a system of equations with no solution? Check all that apply.
What is the solution to the system of equations with the two linear equations shown?
What is the solution to the system of equations with the two linear equations shown?
What is the solution to the system of equations $y = -5x + 3$ and $y = 1$?
What is the solution to the system of equations $y = -5x + 3$ and $y = 1$?
What is the solution to the system of equations $y = -3x - 2$ and $5x + 2y = 15$?
What is the solution to the system of equations $y = -3x - 2$ and $5x + 2y = 15$?
What can Casey conclude from his result of $5=20$ after solving the system of linear equations?
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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