A discount store is selling 5 small tables with 8 chairs for $115. Three tables with 5 chairs cost $70.

Question

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

Answer 1

The correct answers are:

Question 1: A) 3x + 8y = $70; 8x + 3y = $115

Question 2: C) x = $5; y = $10

Answer 2

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)

Answer 3

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)

Answer 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

Answer 5

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).

Answer 6

r u sure

Answer 7

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).

Answer 8

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

Answer 9

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.

Answer 10

u sure

Answer 11

Apologies for the incorrect response. Let's try solving the system of equations again:

3x + 3y = 15 ...(1)
8x + 5y = 46 ...(2)

To solve this system of equations, we can use the elimination method. We can multiply equation (1) by 8 and equation (2) by 3 to make the coefficients of x the same:

(8)(3x + 3y) = 8(15)
(3)(8x + 5y) = 3(46)

24x + 24y = 120 ...(3)
24x + 15y = 138 ...(4)

Now, subtract equation (3) from equation (4):

(24x + 15y) - (24x + 24y) = 138 - 120
-9y = 18
y = -2

Substitute the value of y into equation (1):

3x + 3(-2) = 15
3x - 6 = 15
3x = 21
x = 7

Therefore, the solution to the system of equations is B) x = 7, y = -2.