Solve the system of equations. 3x+y=2 7x−4y=30 (1 point) Responses (−2, 8) left parenthesis negative 2 comma 8 right parenthesis (2, −2) left parenthesis 2 comma negative 2 right parenthesis (12, 12) left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis (2, −4)

Question

Solve the system of equations. 3x+y=2 7x−4y=30 (1 point) Responses (−2, 8) left parenthesis negative 2 comma 8 right parenthesis (2, −2) left parenthesis 2 comma negative 2 right parenthesis (12, 12) left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis (2, −4)

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3 answers
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Answer 1

Bot GPT 3.5 answered
8 months ago

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

From the first equation, we can solve for y:

3x + y = 2
=> y = 2 - 3x

Now we substitute this value of y into the second equation:

7x - 4(2 - 3x) = 30
=> 7x - 8 + 12x = 30
=> 19x - 8 = 30
=> 19x = 38
=> x = 2

We can substitute this value of x back into the first equation to solve for y:

3(2) + y = 2
=> 6 + y = 2
=> y = -4

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

Answer 2

Step-by-Step Bot answered
8 months ago

To solve the system of equations:

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

We'll use the method of substitution.

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

Step 2: Substitute the value of y in Equation 2 with 2 - 3x.
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 38/19
x = 2

Step 3: Substitute the value of x in Equation 1 to find y.
3(2) + y = 2
6 + y = 2
y = 2 - 6
y = -4

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

Answer 3

Explain Bot answered
8 months ago

To solve the system of equations:

1. Begin by using the method of elimination. Multiply the first equation by 4 to make the coefficients of 'y' the same in both equations:
Multiply equation 1: 3x + y = 2 (multiply by 4) --> 12x + 4y = 8

2. Now you have the two equations:
12x + 4y = 8
7x - 4y = 30

3. Add the two equations together to eliminate 'y':
(12x + 4y) + (7x - 4y) = 8 + 30
12x + 7x + 4y - 4y = 38
19x = 38

4. Divide both sides of the equation by 19 to solve for 'x':
19x/19 = 38/19
x = 2

5. Substitute the value of 'x' (which is 2) into either equation to solve for 'y':
Using the first equation: 3x + y = 2
3(2) + y = 2
6 + y = 2
y = 2 - 6
y = -4

So the solution to the system of equations is (x, y) = (2, -4).