Question

Solve the following system of equations by linear combination: 2d + e = 8 d – e = 4

Select one:
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

Answer 1

Because there is a +e and a -e in the two equations we can simply add them together to solve for d...

2d+e+d-e=8+4 combine like terms

3d=12 divide by 3

d=4, now use this d in either original equation to solve for e...d–e=4 so

4-e=4 subtract 4

-e=0

e=0

So the solution, where the lines intersect graphically, is the point (4, 0)