Dealing with linear equations Solve the following SGT Jones

Dealing with linear equations- Solve the following:

SGT Jones is conducting a weapons range for 50 Soldiers. He has a total of 4x Soldiers firing M9s and 6y firing M4s for their qualifications. 55 rounds are needed per person. 3x rounds are needed for zeroing each weapon and 8y rounds are needed for the qualification.

and

Anna has to run 30 miles to complete her marathon. She runs south along the beach 2x miles and then East through a garden 3y miles, to end at Her house. Rico has to run 42 miles to arrive to Annas house. He runs 3x miles North, and 4y miles West.

Solution

soldiers firing M9s + soldiers firing M4s=total soldiers

4x+6y=50

2x+3y=25

Rounds needed for zeroing + round needed for qualification=total rounds

3x+8y=55

So we have two equations

2x+3y=25

3x+8y=55

Multiplying first by 3 and second by -2 and adding both equations

6x+9y-6x-16y=75-110

-7y=-35

y=5

3x+8y=55

3x+40=55

3x=15

x=5

Second question

run along the beach + run through the garden=total run by Anna

2x+3y=30

Rico\'s run in the north direction + Rico\'s run in the west direction= total run by Rico

3x+4y=42

So we have two equations

2x+3y=30

3x+4y=42

Multiply first by 3 and second by -2 and on adding them we get

6x+9y-6x-8y=90-84

y=6

2x+3y=30

2x+18=30

x=6