System A:
7x+4y=-4
5x+8y=28
System B:
7x+4y=-4
?
Which of the following terms will make the systems equivalent?
a. -14x-8y=8
b. 12x+12y=24
c. -12x-12y=24
d. -14x-8y=-8
To determine which term will make the systems A and B equivalent, we need to find the missing equation in System B.
Looking at System A:
7x + 4y = -4 ...(1)
5x + 8y = 28 ...(2)
We can see that to go from Equation (1) to Equation (2), we multiplied both sides of Equation (1) by 5 and Equation (2) by 2. Let's use this information to find the missing equation in System B.
If we multiply Equation (1) by 5, we get:
35x + 20y = -20
If we multiply Equation (2) by 2, we get:
10x + 16y = 56
So, the missing equation in System B is:
35x + 20y = -20.
Comparing this with the given options:
a. -14x - 8y = 8
b. 12x + 12y = 24
c. -12x - 12y = 24
d. -14x - 8y = -8
We can see that none of the given options match the missing equation in System B. Therefore, none of the options will make the systems A and B equivalent.