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.
There is exactly one solution to this system of linear equations and it is (2, 0).
The correct statement is:
There is exactly one solution to this system of linear equations and it is (2, 0).
To determine the solution to the system of equations, we can solve it either by elimination or substitution method. Let's go through each option and see which one correctly describes the solution.
1. "Solve this system by elimination since it is already in standard form and lined up nicely." This statement suggests using elimination method since the equations are already in standard form and aligned properly. However, it appears twice in the options, which means it is redundant.
2. "There is exactly one solution to this system of linear equations and it is (2, 0)." This statement claims that there is only one solution, and it is (2, 0). To determine if it is indeed the solution, we need to substitute these values into the original equations and check if they hold true.
3. "There are infinite solutions to this system of linear equations." This statement suggests that there are infinitely many solutions to the system. To confirm this, we would need to check if the equations are equivalent or if they represent the same line.
4. "These lines are parallel, so there is no solution to this system of linear equations." This statement states that the lines represented by the equations are parallel, which implies that there is no solution. We can determine if the lines are parallel by examining the coefficients of the x and y terms.
5. "There is exactly one solution to this system of linear equations and it is (0, -2)." Similar to option 2, this statement indicates a single solution, which is (0, -2). We can verify this solution by substituting the values into the original equations.
6. "Solve this system by substitution since one of the variables is defined by the other without having to do any math." This option suggests using the substitution method since one variable can be determined directly from the other equation.
Based on the information provided, it appears that options 2 and 5 propose different solutions, while options 3 and 4 suggest there is either an infinite number of solutions or no solution at all. To find the correct solution, we need to solve the system of equations using elimination or substitution.
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.
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.
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.