Question

Solve the system of equations.

3x+y=2
7x−4y=30(1 point)
Responses

(2, −4)
left parenthesis 2 comma negative 4 right parenthesis

(−2, 8)
left parenthesis negative 2 comma 8 right parenthesis

(12, 12)
left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis

(2, −2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use either the substitution method or the elimination method. Let's solve it using the elimination method:

Multiply the first equation by 4 to make the coefficients of y the same in both equations:
12x + 4y = 8

Subtract the second equation from the modified first equation:
(12x + 4y) - (7x - 4y) = 8 - 30
12x + 4y - 7x + 4y = -22
5x + 8y = -22

Now you have a system of equations:
5x + 8y = -22 (Equation 1)
7x - 4y = 30 (Equation 2)

Multiply Equation 1 by 7 and Equation 2 by 5 to make the coefficients of x the same in both equations:
35x + 56y = -154 (Equation 3)
35x - 20y = 150 (Equation 4)

Now subtract Equation 4 from Equation 3:
(35x + 56y) - (35x - 20y) = -154 - 150
35x + 56y - 35x + 20y = -304
76y = -304
y = -4

Now substitute the value of y back into either Equation 1 or Equation 2. Let's use Equation 1:
5x + 8(-4) = -22
5x - 32 = -22
5x = 10
x = 2

Therefore, the solution to the system of equations is (2, -4).

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the system of equations:

3x + y = 2 ...(1)
7x - 4y = 30 ...(2)

We can solve this system of equations using the method of substitution or the method of elimination.
Let's use the method of substitution:
From equation (1), we can rearrange it to solve for y:
y = 2 - 3x ...(3)

Substitute equation (3) into equation (2):
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2

Substitute x = 2 into equation (3) to find y:
y = 2 - 3(2)
y = 2 - 6
y = -4

Therefore, the solution to the system of equations is (2, -4).

Answer 3

[AI-generated answer — Explain Bot]

To solve the system of equations:

1. Begin by writing down the given equations:
3x + y = 2 ...(Equation 1)
7x - 4y = 30 ...(Equation 2)

2. There are multiple methods to solve this system, but we will use the substitution method.

3. Solve Equation 1 for y:
y = 2 - 3x

4. Substitute the value of y in Equation 2:
7x - 4(2 - 3x) = 30

Simplify the equation:
7x - 8 + 12x = 30
19x - 8 = 30

5. Move the constant term to the other side:
19x = 30 + 8
19x = 38

6. Solve for x:
x = 38 / 19
x = 2

7. Substitute the value of x in Equation 1:
3(2) + y = 2
6 + y = 2

8. Solve for y:
y = 2 - 6
y = -4

9. Therefore, the solution to the system of equations is (2, -4).