to solve this system of equation by elimination 6x+5y=2 and 4x +2y=8 to eliminate the x value what do we do?
A- subtract 2 times the second equation from 3 times the first one
B- subtract 3 times the second equation from 2 times the first one
C- subtract 5 times the second equation from 2 times the first one
D- subtract 2 times the second equation from 5 times the first one.
To solve the system of equations 6x + 5y = 2 and 4x + 2y = 8 by elimination, we want to eliminate the x variable.
To do this, we need to manipulate the equations in such a way that when we add or subtract them, the x terms cancel each other out.
Let's examine the given options:
A- subtract 2 times the second equation from 3 times the first one
B- subtract 3 times the second equation from 2 times the first one
C- subtract 5 times the second equation from 2 times the first one
D- subtract 2 times the second equation from 5 times the first one.
For the x terms to cancel out when subtracting the equations, the coefficients of x in both equations must be multiples of each other.
In this case, the coefficients of x in the first equation are 6 and 4, which are not multiples. However, we can eliminate the x variable by multiplying the second equation by 2:
2*(4x + 2y) = 2*8
8x + 4y = 16
Now, the coefficients of x in both equations are 6 and 8, which are multiples of each other.
To eliminate the x terms, we subtract the second equation from the first one:
(6x + 5y) - (8x + 4y) = 2 - 16
6x - 8x + 5y - 4y = -14
-2x + y = -14
Therefore, the correct option to eliminate the x value is:
D- subtract 2 times the second equation from 5 times the first one.