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Two systems of equations are shown: 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? (1 point) -4 2 4 1 -2
To find the value of c that will give the same solution for both systems, we need to compare the coefficients of x and y in both systems.
For the first system, the coefficient of x is 4 and the coefficient of y is 1.
For the second system, the coefficient of x is -4 and the coefficient of y is c.
To get the same solution for both systems, we need the coefficients to be equal. Therefore, we have:
4 = -4
1 = c
From these equations, we can see that the value of c that will give the same solution for both systems is 1.
Therefore, the answer is c = 1.
To find the value of c that would give the same solution for both systems, we need to equate the equations in both systems and solve for c.
First, let's equate the first equation of the first system (4x + y = -1) with the first equation of the second system (8x + 2y = -2).
4x + y = -1 (1)
8x + 2y = -2 (2)
To make the coefficients of y the same in both equations, we can multiply equation (1) by 2:
2(4x + y) = 2(-1)
8x + 2y = -2 (3)
Comparing equation (3) with equation (2), we see that they are identical. Therefore, c would need to be 2 in order to get the same solution for both systems.
So, the correct answer is c = 2.
To find the value of c that would result in the same solution for both systems, we need to solve the two systems of equations separately and then compare the solutions.
Let's start by solving the first system of equations:
1) 4x + y = -1
2) x + y = 2
We can solve this system by using the method of substitution or elimination. Let's use the method of substitution:
From equation 2), we can solve for y:
y = 2 - x
Substituting this expression for y in equation 1), we get:
4x + (2 - x) = -1
4x + 2 - x = -1
3x = -3
x = -1
Now substitute the value of x = -1 back into equation 2) to solve for y:
-1 + y = 2
y = 3
So, the solution to the first system of equations is x = -1 and y = 3.
Now let's solve the second system of equations:
1) 8x + 2y = -2
2) -4x + cy = -8
Similarly, we can solve this system using the method of substitution:
From equation 2), we can solve for cy:
cy = -8 + 4x
cy = 4x - 8
y = (4x - 8) / c
Substituting this expression for y in equation 1), we get:
8x + 2 * ((4x - 8) / c) = -2
8x + (8x - 16) / c = -2
Now, to get the same solution for both systems, we need the x and y values to be the same. So, comparing the x values from both systems, we have:
For the first system: x = -1
For the second system: 8x + (8x - 16) / c = -2
Substituting x = -1 into the equation for the second system, we get:
8(-1) + (8(-1) - 16) / c = -2
-8 + (-8 - 16) / c = -2
-8 - 24 / c = -2
-8c - 24 = -2c
6c = -24
c = -4
Therefore, the value of c that would result in the same solution for both systems of equations is c = -4.