Question

Solve the following system of equations by linear combination:

2d + e = 8


d - e = 4

A. The solution is (5, -2)

B. There is no solution

C. There are an infinite number of solutions

D. The solution is (4, 0)

Answer 1

`\underline{+\left\{\begin{array}{ccc}2d+e=8\\d-e=4\end{array}\right}\ \ \ |\text{add both sides of the equations}\\.\ \ \ \ \ \ 3d=12\ \ \ \ |:3\\.\ \ \ \ \ \ d=4\\\\\text{put the value of d to the first equation}\\\\2(4)+e=8\\8+e=8\ \ \ |-8\\e=0\\\\\text{Answer:}\ D.\ The\ solution\ is (4,\ 0).`