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)
Responses
4
4
1
1
-2
-2
2
2
-4
Your solution does not work.
The solution to
4x+y=−1
x+y=2
is (-1,3)
Note that this is also the solution to
8x+2y=−2
So now all we need is to find c such that
−4(-1)+3c=−8
c = -16/3
Not one of the choices. I suspect a typo.
You are correct, I apologize for the mistake in my previous response. Thank you for pointing it out.
To find the value of c that would give the same solution for both systems, we need to equate the values of y in both systems.
In the first system, we have x + y = 2. Solving for y, we get y = 2 - x.
In the second system, we have −4x + cy = −8. To have the same solution for y, we need the coefficients of y to be the same. Comparing the second equations in both systems, we see that the coefficient of y in the first system is 1, while the coefficient of y in the second system is c.
To equate the coefficients, we can set c = 1.
Therefore, the value of c that would give the same solution for both systems is 1.
To find the value of c that makes both systems have the same solution, we need to compare the slopes of the two systems. The slopes of the equations in the first system are 4 and 1 (coefficient of x in the first equation and coefficient of x in the second equation, respectively). The slopes of the equations in the second system are 8 and -4 (coefficient of x in the first equation and coefficient of x in the second equation, respectively).
To get the same solution for both systems, the slopes must be equal. Therefore, we can set up the following equation:
4 = 8c
To solve for c, divide both sides of the equation by 8:
c = 4/8 = 1/2
Therefore, the value of c that would make both systems have the same solution is 1/2.
To find the value of c that would give the same solution for both systems of equations, we need to compare the coefficients of y in each system.
In the first system, the coefficient of y is 1 (from the equation x + y = 2).
In the second system, we have -4x + cy = -8. Since y appears with coefficient c in this equation, we need to find the value of c that would make the coefficient of y the same as in the first system.
From the two equations, we have:
1) 4x + y = -1
2) -4x + cy = -8
To make the coefficients of y the same in both systems, we equate the coefficients:
1 = c
Therefore, the value of c that would give the same solution for both systems is 1.
To find the value of c that would give the same solution for both systems, we need to equate the values of y in both systems.
In the first system, we have x + y = 2. Solving for y, we get y = 2 - x.
In the second system, we have -4x + cy = -8. To have the same solution for y, we need the coefficients of y to be the same. Comparing the second equations in both systems, we see that the coefficient of y in the first system is 1, while the coefficient of y in the second system is c.
To equate the coefficients, we can set c = 1.
Therefore, the value of c that would give the same solution for both systems is 1.