In order for the two systems of equations to have the same solution, the coefficients of the corresponding variables in each equation must be proportional.
Comparing the first equation of the first system (4x + y = -1) to the first equation of the second system (8x + 2y = -2), we can see that the coefficient of x in the first equation is half of the coefficient of x in the second equation (4x vs 8x).
Similarly, the coefficient of y in the first equation is also half of the coefficient of y in the second equation (1y vs 2y).
Therefore, the value of c needs to be 2 in order for both systems to have the same solution.
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
-4
-4
1
1
2
2
-2
1 answer