Question

Solve the system of equations using elimination. 4x - 7y = 5, 9x – 7y = –15 Responses A (3, 4)(3, 4) B (4, 3)(4, 3) C (-3, 4)(-3, 4) D (-4, 3)(-4, 3) E (-4, -3)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations using elimination, we need to eliminate one of the variables by adding or subtracting the two equations. Adding the equations directly does not eliminate any variables, but if we multiply the second equation by 4, we can eliminate the y variable:

4x - 7y = 5
(4)(9x – 7y) = (4)(–15)
36x - 28y = -60

Now, subtract the first equation from the second equation:

(36x - 28y) - (4x - 7y) = -60 - 5
36x - 28y - 4x + 7y = -65
32x - 21y = -65

We now have a new equation:

32x - 21y = -65

Now, we can solve the new equation and find the value of x:

32x - 21y = -65
32x = 21y - 65
x = (21y - 65)/32

To find the value of y, substitute the expression for x into one of the original equations:

4x - 7y = 5
4((21y - 65)/32) - 7y = 5
(21y - 65)/8 - 7y = 5
21y - 65 - 56y = 40
-35y = 105
y = -3

Now, substitute the value of y back into the expression for x:

x = (21(-3) - 65)/32
x = (-63 - 65)/32
x = -128/32
x = -4

Therefore, the solution to the system of equations is (-4, -3). The correct answer choice is E.

Answer 2

6x + 3y = 9 2x + 3y = 1 Solve the system of equations. Responses A x = 2, y = -1x = 2, y = -1 B x = -1, y = 2x = -1, y = 2 C x = - , y = 3x = - 1 2 , y = 3 D x = 3, y = - x = 3, y = -1/2 E x = 1, y = 1

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use elimination. Subtracting the second equation from the first equation will eliminate the y variable:

(6x + 3y) - (2x + 3y) = 9 - 1
6x - 2x + 3y - 3y = 8
4x = 8
x = 8/4
x = 2

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's substitute it into the first equation:

6x + 3y = 9
6(2) + 3y = 9
12 + 3y = 9
3y = 9 - 12
3y = -3
y = -3/3
y = -1

Therefore, the solution to the system of equations is (x = 2, y = -1). The correct answer choice is A.

Answer 4

Solve the system of equations using elimination. 8x + 7y = -16 10x + 7y = -6 Responses A (3, 6)(3, 6) B (8, 5)(8, 5) C (7, 10)(7, 10) D (5, -8)(5, -8) E (-5, -8)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations using elimination, we can subtract the first equation from the second equation to eliminate the variable y:

(10x + 7y) - (8x + 7y) = -6 - (-16)
10x - 8x + 7y - 7y = 10
2x = 10
x = 10/2
x = 5

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's substitute it into the first equation:

8x + 7y = -16
8(5) + 7y = -16
40 + 7y = -16
7y = -16 - 40
7y = -56
y = -56/7
y = -8

Therefore, the solution to the system of equations is (x = 5, y = -8). The correct answer choice is D.

Answer 6

5x - 2y = 3 -5x + 4y = 9 Solve the system of equations. Responses A x = 6, y = 3x = 6, y = 3 B x = 6, y = 13 1/2x = 6, y = 13 1 2 C x = 3, y = 6x = 3, y = 6 D x = 1, y = 0x = 1, y = 0 E x = -3, y = -6

Answer 7

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations using elimination, we can add the two equations to eliminate the x variable:

(5x - 2y) + (-5x + 4y) = 3 + 9
5x - 5x - 2y + 4y = 12
2y = 12
y = 12/2
y = 6

Now that we found the value of y, we can substitute it back into one of the original equations to solve for x. Let's substitute it into the first equation:

5x - 2y = 3
5x - 2(6) = 3
5x - 12 = 3
5x = 3 + 12
5x = 15
x = 15/5
x = 3

Therefore, the solution to the system of equations is (x = 3, y = 6). The correct answer choice is C.