A discount store is selling 5 small tables with 8 chairs for $115. Three tables with 5 chairs cost $70.
Question 1
Which system of linear equations could be used to find the cost of each table (x) and the cost of each chair (y)?
Responses
A 3x + 8y = $70; 8x + 3y = $1153x + 8y = $70; 8x + 3y = $115
B 5x + 8y = $115; 3x + 5y = $705x + 8y = $115; 3x + 5y = $70
C 5x + 8y = $115; 2x − 5y = $705x + 8y = $115; 2x − 5y = $70
D 8x + 5y = $115; 5x + 3y = $708x + 5y = $115; 5x + 3y = $70
Question 2
Determine the cost of each table (x) and the cost of each chair (y).
Responses
A x = $15; y = $5x = $15; y = $5
B x = $10; y = $5x = $10; y = $5
C x = $5; y = $10x = $5; y = $10
D x = $12; y = $3
The correct answers are:
Question 1: A) 3x + 8y = $70; 8x + 3y = $115
Question 2: C) x = $5; y = $10
x = y - 3
x + 3y = 13
What is the solution to the system of equations?
Responses
A (1, 4)(1, 4)
B (4, 1)(4, 1)
C (7, 4)(7, 4)
D (2.5, 5.5)(2.5, 5.5)
E (5.5, 2.5)
To find the solution to the system of equations, we can substitute the value of x from the first equation into the second equation:
x + 3y = 13
(y - 3) + 3y = 13
4y - 3 = 13
4y = 16
y = 4
Now, we can substitute the value of y back into the first equation to solve for x:
x = y - 3
x = 4 - 3
x = 1
Therefore, the solution to the system of equations is A) (1, 4)
What is the solution to the system of equations?
-2x + y = -5
3x – 2y = 12
Responses
A (3, 1)(3, 1)
B (6, 3)(6, 3)
C (-2, -9)(-2, -9)
D (-2, -1)(-2, -1)
E no solution
To find the solution to the system of equations, we can use either substitution or elimination method.
Let's use the elimination method to solve this system:
-2x + y = -5 (Multiply the equation by 2)
3x - 2y = 12
-4x + 2y = -10
3x - 2y = 12
Now, add the two equations:
-4x + 2y + 3x - 2y = -10 + 12
Simplifying, we get:
-x = 2
x = -2
Substitute the value of x into one of the original equations:
-2x + y = -5
-2(-2) + y = -5
4 + y = -5
y = -9
Therefore, the solution to the system of equations is C) (-2, -9).
r u sure
Apologies for the incorrect response. Let's try solving the system of equations again:
-2x + y = -5 ...(1)
3x - 2y = 12 ...(2)
We can solve this system by using the elimination method:
Multiply equation (1) by 2:
-4x + 2y = -10 ...(3)
Now, let's add equation (2) and equation (3):
(3x - 2y) + (-4x + 2y) = 12 + (-10)
-x = 2
x = -2
Substitute the value of x into equation (1):
-2(-2) + y = -5
4 + y = -5
y = -9
The solution to the system of equations is C) (-2, -9).
3x + 3y = 15
8x + 5y = 46
What is the solution to the system of equations above?
Responses
A x = -3, y = 6x = -3, y = 6
B x = 7, y = -2x = 7, y = -2
C x = 6, y = -4x = 6, y = -4
D x = -2, y = -6
To find the solution to the system of equations, we can solve it using either substitution or elimination method.
Let's use the elimination method to solve this system:
Multiply equation (1) by 5 and equation (2) by 3 to make the coefficients of y the same:
15x + 15y = 75 ...(3)
24x + 15y = 138 ...(4)
Now, subtract equation (3) from equation (4):
(24x + 15y) - (15x + 15y) = 138 - 75
9x = 63
x = 7
Substitute the value of x into equation (1):
3(7) + 3y = 15
21 + 3y = 15
3y = 15 - 21
3y = -6
y = -2
Therefore, the solution to the system of equations is B) x = 7, y = -2.