The Woodson and Baker families went to the Burger Shack for dinner. The Woodsons bought 3 burger meals and 4 hot dog meals for $48. The Bakers bought 6 burger meals and 2 hot dog meals for $60. How much does each meal cost? Show your work.
If x represents the cost of burger meals, then y represents ?
The system of linear equations would look like ?
How much does a burger meal cost?
How much does a hot dog meal cost?
The total $ spent on both meals
The number of hot dog meals
The cost of a hot dog meal
3x + 6y = 48 and 6x + 4y = 60
3x + 4y = 48 and 6x + 2y = 60
48x + 60y = 9x + 6y
$4
$6
$8
$9
$5
If x represents the cost of burger meals, then y represents the cost of a hot dog meal.
The system of linear equations would look like:
3x + 4y = 48
6x + 2y = 60
To solve for x and y, we can multiply the first equation by 2 and the second equation by 2 to eliminate y:
6x + 8y = 96
12x + 4y = 120
Subtracting the second equation from the first equation gives:
-6x + 4y = -24
Dividing both sides by -2, we get:
3x - 2y = 12
Adding this equation to the second equation gives:
6x + 2y = 60
3x - 2y = 12
-------------
9x = 72
x = 8
Therefore, a burger meal costs $8. To find the cost of a hot dog meal, we can substitute x = 8 into the first equation:
3(8) + 4y = 48
24 + 4y = 48
4y = 24
y = 6
Therefore, a hot dog meal costs $6.
The total $ spent on both meals would be:
3(8) + 4(6) = $24 + $24 = $48
Therefore, the answers are:
- The cost of a burger meal: $8
- The cost of a hot dog meal: $6
Select the statement that correctly describes the solution to this system of equations. 8x − 2y = −4 4x − y = −2
There is no solution.
There are infinitely many solutions.
There is exactly one solution at (0,–2).
There is exactly one solution at (2,0).
To solve this system of equations, we can use either substitution or elimination method. Let's use the elimination method here.
Given equations:
1) 8x - 2y = -4
2) 4x - y = -2
Let's multiply the second equation by 2 to make the coefficients of y the same:
1) 8x - 2y = -4
2) 8x - 2y = -4
Now, subtract the second equation from the first:
8x - 2y - (8x - 2y) = -4 - (-4)
0 = 0
Since we got 0 = 0, it means these two equations are actually the same line. This means there are infinitely many solutions because the two equations represent the same line, meaning they intersect at every point along that line.
Therefore, the correct statement is: There are infinitely many solutions.
The solution to a system of two linear equations is x = 3; y = 9.
How could the intersection of the graphs of the two equations be located on a coordinate grid?
What does the solution to a system of two linear equations mean on the graph?
Can you have more than one solution to a Linear system of equations?
Can you have exactly two solutions to a Linear system of equations?
Can you have no solutions to a Linear system of equations?
from the origin, move 3 units up and 9 units right
from the origin, move 3 units right and 9 units up
the point where the lines cross the y-axis
the point of intersection of the two lines
the point that the two lines DO NOT have in common
yes, if both lines are the exact same line
yes, if the lines are parallel
no, because lines are straight
yes, because the lines could cross each other twice
- The intersection of the graphs of two linear equations can be located on a coordinate grid where the x-coordinate is 3 and the y-coordinate is 9.
- The solution to a system of two linear equations represents the point of intersection on the graph where both lines coincide. It is the point at which the two lines intersect.
- Yes, you can have more than one solution to a linear system of equations. This can happen if the two lines are the same line, resulting in infinite intersection points.
- No, you cannot have exactly two solutions to a linear system of equations. The system would either have one unique solution, infinite solutions, or no solution.
- Yes, you can have no solutions to a linear system of equations. This occurs when the two lines are parallel and do not intersect.
- The point of intersection of the two lines represents the solution to the system of equations, which is x = 3 and y = 9.
bot i'm confused
I apologize for any confusion. Let me clarify:
- If the solution to a system of two linear equations is x = 3 and y = 9, this means that the point of intersection of the two lines that represent these equations is located at (3, 9) on the coordinate grid.
- When the lines of two linear equations intersect, the point of intersection is the solution to the system of equations. In this case, the solution is x = 3 and y = 9.
- You can have more than one solution to a linear system of equations if the lines are the same line, resulting in an infinite number of intersection points.
- You cannot have exactly two solutions to a linear system of equations. The system would either have one unique solution, infinite solutions, or no solution.
- You can have no solutions to a linear system of equations if the lines are parallel and do not intersect.
Hopefully, this clears things up. Let me know if you have any more questions or need further clarification.
bot use the answers provided to answer the questions
I apologize for the confusion earlier. Here are the answers using the options provided:
1. How could the intersection of the graphs of the two equations be located on a coordinate grid?
- The point of intersection of the two lines (the solution) is at the point where the lines have in common, so the answer is "the point of intersection of the two lines."
2. What does the solution to a system of two linear equations mean on the graph?
- The solution represents the point where the two lines intersect.
3. Can you have more than one solution to a Linear system of equations?
- Yes, if both lines are the exact same line.
4. Can you have exactly two solutions to a Linear system of equations?
- No, because the lines are straight.
5. Can you have no solutions to a Linear system of equations?
- Yes, if the lines are parallel.
If you have any more questions or need further clarification, feel free to ask.