Two systems of equations are shown:

Question

4x+y=−1
x+y=2
and
8x+2y=−2
−4x+cy=−8
What would the value of c need to be to get the same solution for both systems? (

Responses
2
1
4
-4
-2

Answer 1

In order for the two systems of equations to have the same solution, the coefficients of y in both systems must be the same.

In the first system of equations, the coefficient of y is 1. In the second system of equations, the coefficient of y is c.

To make the two systems have the same solution, the value of c must be equal to 1.

Therefore, the correct answer is 1.

Answer 2

which one is right???????

Answer 3

Apologies for the incorrect response earlier. The correct answer is c = -4.

By substituting the values of x and y from the first system into the second system, we get:
-4(-1) + (-4)y = -8
4 - 4y = -8
-4y = -12
y = 3

Therefore, with c = -4, the second system becomes:
8x + 2y = -2
-4x - 4y = -8

Simplifying the second equation:
-4x - 4y = -8
-4x - 4(3) = -8
-4x - 12 = -8
-4x = 4
x = -1

So, the solution to the second system is x = -1 and y = 3, which is the same as the solution to the first system.

Again, I apologize for the confusion earlier, and the correct answer is c = -4.

Answer 4

r u sure?

Answer 5

My apologies for the confusion. I made an error in my previous response. Let's go through the solution again to find the correct value of c.

First, let's solve the first system of equations:
4x + y = -1 ...(1)
x + y = 2 ...(2)

We can solve this system by using the method of substitution. From equation (2), we can express y in terms of x:
y = 2 - x

Substituting this expression for y into equation (1), we get:
4x + (2 - x) = -1
4x + 2 - x = -1
3x = -3
x = -1

Substituting the value of x into equation (2), we can solve for y:
-1 + y = 2
y = 3

So, the solution to the first system is x = -1 and y = 3.

Now, let's solve the second system of equations:
8x + 2y = -2 ...(3)
-4x + cy = -8 ...(4)

We want to find the value of c that will give the same solution as the first system.

Substituting the values of x and y from the first system into the second system, we get:
-4(-1) + c(3) = -8
4 + 3c = -8
3c = -12
c = -4

Therefore, the correct value of c that would give the same solution for both systems is c = -4.

Apologies again for the confusion, and the correct answer is c = -4.

Answer 6

are u sure its -4

Answer 7

Apologies for the confusion. Let's go through the solution again to find the correct value of c.

First, let's solve the first system of equations:
4x + y = -1 ...(1)
x + y = 2 ...(2)

We can solve this system by using the method of elimination. By subtracting equation (2) from equation (1), we eliminate y:
(4x + y) - (x + y) = (-1) - 2
3x = -3
x = -1

Substituting the value of x into equation (2), we can solve for y:
(-1) + y = 2
y = 3

So, the solution to the first system is x = -1 and y = 3.

Now, let's solve the second system of equations:
8x + 2y = -2 ...(3)
-4x + cy = -8 ...(4)

We need to find the value of c that will make this system have the same solution as the first system.

Substituting the values of x and y from the first system into the second system, we get:
-4(-1) + c(3) = -8
4 + 3c = -8
3c = -12
c = -4

Therefore, the value of c that would give the same solution for both systems is -4.

Again, I apologize for the confusion earlier, and the correct answer is c = -4.