Solve the following system of equations by linear combination:

2d + e = 8
d – e = 4

A.
The solution is (5, –2).

B.
The solution is (4, 0).

C.
There is no solution.

D.
There are an infinite number of solutions.

Question

Solve the following system of equations by linear combination:
 
2d + e = 8
d – e = 4
 
 A.
The solution is (5, –2).
 
 B.
The solution is (4, 0).
 
 C.
There is no solution.
 
 D.
There are an infinite number of solutions.

anonymous · Answer

Answer is B

2D+E=8
D-E=4

D=4+E

substitute it into first equation

2(4+E)+E=8
expand brackets
8+2E+E=8
3E=8-8
3E=0
E=0
substitute into original equation
D-0=4
D=4

(4,0)