Solve the system of equations.

Question

Solve the system of equations.

3x+y=2
7x−4y=30 (1 point)
Responses

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

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3 answers
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Answer 1

Bot GPT 3.5 answered
1 year ago

To solve the system of equations, we can use the method of elimination by multiplying the first equation by 4 to eliminate y:

4(3x+y) = 4(2)
12x + 4y = 8

Now we have the system of equations:
12x + 4y = 8
7x - 4y = 30

Adding the two equations together, we get:
(12x + 4y) + (7x - 4y) = 8 + 30
19x = 38
x = 2

Substituting x = 2 into the first equation, we get:
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
1 year ago

To solve the system of equations:

1. Start with the given equations:
Equation 1: 3x + y = 2
Equation 2: 7x − 4y = 30

2. Now, we can solve this system of equations using the method of substitution or elimination. Let's use the method of substitution:

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

b. Substitute the value of y from Equation 1 into Equation 2:
7x - 4(2 - 3x) = 30

c. Simplify and solve for x:
7x - 8 + 12x = 30
19x = 38
x = 2

d. Substitute the value of x into Equation 1 to solve for y:
3(2) + y = 2
6 + y = 2
y = -4

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

Answer 3

Explain Bot answered
1 year ago

To solve the system of equations, we can use the method of substitution or elimination. I will explain how to solve it using the method of substitution.

Step 1: Solve one of the equations for a variable.
Let's solve the first equation, 3x + y = 2, for y in terms of x:
y = 2 - 3x.

Step 2: Substitute the expression for y into the second equation.
Substitute y = 2 - 3x into the second equation, 7x - 4y = 30:
7x - 4(2 - 3x) = 30.

Step 3: Simplify and solve for x.
Expand the equation:
7x - 8 + 12x = 30.
Combine like terms:
19x - 8 = 30.
Add 8 to both sides:
19x = 38.
Divide both sides by 19:
x = 2.

Step 4: Substitute the value of x back into one of the original equations to solve for y.
Substitute x = 2 into the first equation, 3x + y = 2:
3(2) + y = 2,
6 + y = 2.
Subtract 6 from both sides:
y = -4.

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