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

the solution is (2,-1)

Answer 2

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

$\frac{10d}{10} =\frac{10}{10}$

$d=1$

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