Answer:
B) Subtract the bottom equation from the top equation.
C) Add the equations.
Explanation:
Let us analyze each of the options to see which one of them work.
A) Multiply the top equation by 7, then subtract the bottom equation from the top equation.
Multiplying the top equation by 7 gives:
7 * (16x + 5y) = (1 * 7)
112x + 35y = 7
Then, subtracting the bottom equation from this:
112x + 35y = 7
- (16x - 5y = 7)
=> 112x + 35y - 16x + 5y = 7 - 7
112x - 16x + 35y + 5y = 0
96x + 40y = 0
This method didn't eliminate any variable, so it didn't work for us.
B) Subtract the bottom equation from the top equation
This will yield:
16x + 5y = 1
- (16x - 5y = 7)
=> 16x + 5y - 16x + 5y = 1 - 7
16x - 16x + 5y + 5y = -6
0x + 10y = -6
10y = -6
y = -6 / 10
Hence, one variable has been eliminated. It works.
C) Add the equations
This yields:
16x + 5y = 1
+ 16x - 5y = 7
32x + 0y = 8
32x = 8
=>x = 8 / 32 = 1 / 4
This method works since one variable has been eliminated.