Solve the following system of equations by linear combination: 2d – e = 7 d + e = 5 a. the solution is (4, 1). b. there are an infinite number of solutions. c. the solution is (3, –1). d. there is no solution.

The solution is (4, 1).

Step-by-step explanation:

For the first multiply the second equation by -1 then add them together.  

4x + y = 5  

-1( 3x + y = 3)  

4x + y = 5  

-3x - y = -3  

x=2  

Plug that in and you get -3 for y  

Answer is (2,-3)  

For the second, just add them  

2d – e = 7  

d + e = 5  

3d=12  

d=4  

Plug that into either equation and e is 1  

The solution is (4, 1).

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