elimination method

Question

To use the elimination method, you can subtract the two equations in a system of equations to eliminate one of the variables.

Subtract the two equations.

{x+y=7

{x−3y=5

What is the resulting equation?

A 2x - 2y = 2

B 0 + 4y = 12

C 0 + 4y = 2

D 2x + 4y = 12 

Answer 1

x + y = 7

x −3y =5

---------------- (elimination: subtract equations)

4y = 2 (Answer C)

y = 1/2

Substitute 1/2 for y in either equation to find x.

x + 1/2 = 7

x = 6 1/2

Answer 2

The answer is C arrived at as follows:

x + y = 7

-(x - 3y = 5) (We are multiplying the 2nd equation by -1 and then adding it to the 1st equation.)

x + y = 7

-x + 3y = -5

----------------

0 + 4y = 2

From here we obtain y = 1/2 and then x = 13/2