Question

if 5/2 x + y = 2

x + 2/3y=4

if (x,y) is a solution to the systems of equations what is the value of x?

4
-4
12
-12
no solution exist

correct answer?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations, we can use the method of substitution.

From the first equation, we can isolate y:

5/2x + y = 2
y = 2 - 5/2x

Now, substitute this expression for y in the second equation:

x + 2/3(2 - 5/2x) = 4
x + 4/3 - 5/3x = 4
-2/3x + 4/3 = 4
-2/3x = 4 - 4/3
-2/3x = 12/3 - 4/3
-2/3x = 8/3
x = (8/3) / (-2/3)
x = (8/3) * (-3/2)
x = -4

Therefore, the value of x is -4.

The correct answer is -4.

Answer 2

x+3y=5

-x=6y=4

solve the system of equations correct answer only

Answer 3

[AI-generated answer — Bot GPT 3.5]

The second equation you provided, "-x = 6y = 4," appears to have a typing error. Specifically, there is an extra equal sign between "6y" and "4."

Could you please confirm the correct equation or provide the correct equation so that I can assist you in solving the system?

Answer 4

x=1 y=2

x=2 y=1
x=1 y=1
x=0 y=2
x=6 y=1

Answer 5

[AI-generated answer — Bot GPT 3.5]

Let's solve the system of equations:

Equation 1: x + 3y = 5
Equation 2: x + 6y = 4

To solve this system using the method of substitution, we can start by isolating x from Equation 1:

x = 5 - 3y

Substitute this value of x into Equation 2:

5 - 3y + 6y = 4

Combine like terms:

3y + 5 = 4

Subtract 5 from both sides:

3y = 4 - 5
3y = -1

Divide both sides by 3:

y = -1/3

Now, substitute this value of y back into Equation 1 to solve for x:

x + 3(-1/3) = 5
x - 1 = 5

Add 1 to both sides:

x = 5 + 1
x = 6

Therefore, the solution to the system of equations is x = 6 and y = -1/3.

The correct answer is x = 6 and y = -1/3.

Answer 6

thats not an answer choice????

Answer 7

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. Let's solve the system of equations again:

Equation 1: x + 3y = 5
Equation 2: -x + 6y = 4

We can solve this system by either the substitution method or the elimination method. Here, we will use the elimination method to solve the system:

Multiply Equation 1 by -1 to make the x terms add up to zero:
-1(x + 3y) = -1(5)
-x - 3y = -5

Now, add the two equations together:
(-x + 6y) + (-x - 3y) = 4 + (-5)
-2x + 3y = -1

Now, we have a new equation:
-2x + 3y = -1 (Equation 3)

Now, let's solve Equation 3 along with Equation 2 to find the values of x and y:

(-2x + 3y) - (-x + 6y) = -1 - 4
-2x + 3y + x - 6y = -5
-x - 3y = -5 (Equation 4)

Equation 3: -2x + 3y = -1
Equation 4: -x - 3y = -5

Add the two equations together:
(-2x + x) + (3y - 3y) = (-1) + (-5)
-x = -6

Divide both sides by -1:
x = 6

Now substitute the value of x into Equation 1 to find the value of y:

6 + 3y = 5
3y = 5 - 6
3y = -1
y = -1/3

Therefore, the solution to the system of equations is x = 6 and y = -1/3.

The correct answer is x = 6 and y = -1/3.

Answer 8

DUDE I JUST SAID THATS NOT AN ANSWER CHOICE

Answer 9

[AI-generated answer — Bot GPT 3.5]

Apologies for the oversight. Let's solve the system of equations again:

Equation 1: x + 3y = 5
Equation 2: -x + 6y = 4

To eliminate x, we can multiply Equation 1 by -1 and add it to Equation 2:

-1(x + 3y) = -1(5)
-x - 3y = -5

Adding the two equations:

(-x + 6y) + (-x - 3y) = 4 + (-5)
-2x + 3y = -1

Multiplying Equation 1 by 2:

2(x + 3y) = 2(5)
2x + 6y = 10

Now, we have a new system of equations:

-2x + 3y = -1
2x + 6y = 10

Adding these equations, we can eliminate x:

(-2x + 3y) + (2x + 6y) = -1 + 10
9y = 9
y = 1

Now, substitute the value of y into Equation 1 to find x:

x + 3(1) = 5
x + 3 = 5
x = 5 - 3
x = 2

Therefore, the solution to the system of equations is x = 2 and y = 1.

The correct answer is x = 2 and y = 1.