Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations: 8x−2y=−4 4x−y=−2 (2 points) Responses Solve this system by elimination since it is already in standard form and lined up nicely. Solve this system by elimination since it is already in standard form and lined up nicely. There is exactly one solution to this system of linear equations and it is (2, 0). There is exactly one solution to this system of linear equations and it is (2, 0). There are infinite solutions to this system of linear equations. There are infinite solutions to this system of linear equations. These lines are parallel, so there is no solution to this system of linear equations. These lines are parallel, so there is no solution to this system of linear equations. There is exactly one solution to this system of linear equations and it is (0, -2). There is exactly one solution to this system of linear equations and it is (0, -2). Solve this system by substitution since one of the variables is defined by the other without having to do any math.
5 answers
There is exactly one solution to this system of linear equations and it is (2, 0).
is there only one answer or are multiple correct
Apologies for the confusion. Upon reviewing the options again, it seems that there is only one correct statement:
There is exactly one solution to this system of linear equations and it is (2, 0).
This statement correctly describes the solution to the given system of equations.
There is exactly one solution to this system of linear equations and it is (2, 0).
This statement correctly describes the solution to the given system of equations.
Jim bought some potted plants: Petunias cost $11 per pot and Begonias cost $15 per pot. Jim bought 19 potted plants in all and spent a total of $225 on the plants. Which would be a correct statement?
Jim bought 15 petunias. Jim bought 15 petunias. Jim bought 15 begonias. Jim bought 15 begonias. Jim bought 4 petunias. Jim bought 4 petunias. Jim bought 18 begonias.
Jim bought 15 petunias. Jim bought 15 petunias. Jim bought 15 begonias. Jim bought 15 begonias. Jim bought 4 petunias. Jim bought 4 petunias. Jim bought 18 begonias.
To determine the correct statement, we need to set up and solve a system of equations based on the given information.
Let P represent the number of Petunias Jim bought, and B represent the number of Begonias Jim bought.
From the problem, we know:
1) The total number of potted plants Jim bought is 19: P + B = 19.
2) The total amount spent by Jim on the plants is $225: 11P + 15B = 225.
To find the correct statement, we can substitute different values for P and B into the equations and see which one satisfies both equations simultaneously.
1) Jim bought 15 petunias: If P = 15, then B = 19 - P = 19 - 15 = 4. However, the second equation does not hold true: 11(15) + 15(4) = 165 + 60 = 225 ≠ 225.
2) Jim bought 15 begonias: If B = 15, then P = 19 - B = 19 - 15 = 4. Again, the second equation does not hold: 11(4) + 15(15) = 44 + 225 = 269 ≠ 225.
3) Jim bought 4 petunias: If P = 4, then B = 19 - P = 19 - 4 = 15. Once again, the second equation does not hold: 11(4) + 15(15) = 44 + 225 = 269 ≠ 225.
4) Jim bought 18 begonias: If B = 18, then P = 19 - B = 19 - 18 = 1. The second equation still does not hold: 11(1) + 15(18) = 11 + 270 = 281 ≠ 225.
None of the provided statements is correct based on the information given.
Let P represent the number of Petunias Jim bought, and B represent the number of Begonias Jim bought.
From the problem, we know:
1) The total number of potted plants Jim bought is 19: P + B = 19.
2) The total amount spent by Jim on the plants is $225: 11P + 15B = 225.
To find the correct statement, we can substitute different values for P and B into the equations and see which one satisfies both equations simultaneously.
1) Jim bought 15 petunias: If P = 15, then B = 19 - P = 19 - 15 = 4. However, the second equation does not hold true: 11(15) + 15(4) = 165 + 60 = 225 ≠ 225.
2) Jim bought 15 begonias: If B = 15, then P = 19 - B = 19 - 15 = 4. Again, the second equation does not hold: 11(4) + 15(15) = 44 + 225 = 269 ≠ 225.
3) Jim bought 4 petunias: If P = 4, then B = 19 - P = 19 - 4 = 15. Once again, the second equation does not hold: 11(4) + 15(15) = 44 + 225 = 269 ≠ 225.
4) Jim bought 18 begonias: If B = 18, then P = 19 - B = 19 - 18 = 1. The second equation still does not hold: 11(1) + 15(18) = 11 + 270 = 281 ≠ 225.
None of the provided statements is correct based on the information given.