Question

{3d−e=7d+e=5 Use the linear combination method. The solution is (3, 2). There is no solution. The solution is (2, −1). There are infinitely many solutions.

Answer 1

we are given system of equation as

`3d-e=5`

`7d+e=5`

We are given linear combination method

In linear combination method , we always try to cancel one variable by combining two equations

step-1: Add both equations

`3d-e=5`

`7d+e=5`

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

`7d+3d=5+5`

`10d=10`

step-2: Divide both sides by 10

`(10d)/(10) =(10)/(10)`

`d=1`

step-3: Solve for e

`7d+e=5`

we can plug d=1

`7*1+e=5`

`7+e-7=5-7`

`e=-2`

so, solution is (d,e)=(1,-2)..........Answer