Question

Part 1:
For the following system of equations, write your own real world scenario that describes what is happening. Use complete sentences and correct grammar in your scenario.

Part 2:
Solve the system and explain what the results mean according to your scenario.

2x + y = 10
3x + 4y = 25

Answer 1

just a thought, algebra and system of algebraic equations is useful in the field of economics. .

Answer 2

we want either x's or y's to be equal and opposite to cancel: so we try x's.
(x-3) -6x -3y = -30 muliply across by -3
(x +2) 6x +8y= 50 multiply across by +2
result:
-6x and 6x cancel
-3y+8y=5y
-30+50=20
that is:
5y=20
y=20/5
y=4
substitute y=4 in eq 1.
2x+y=10
2x+(4)=10
2x=10-4
2x=6
x=6/2
x=3

check in 2nd eq for x=3, y=4
3(3)+4(4)=25
9+16=25
25=25 Q.E.D.

Answer 3

thank you

Answer 4

@BPDlkeme , where is the real world scenario there?

Answer 5

well if you re-arrange the equations (which are linear equations, i.e. equations of the first degree) then the solution x=3, y=4 represents where these two lines cross. A real world example using these types of equations could be taken from linear programming. Say for example you produce x widgets, obviously the more x widgets you produce, the higher the cost. if this was shown graphically (cost vs units produced) it could represent one line, and on the other you might have profit v sales (snother linear equation. Where the two lines intersect (x=3, y=4) would be your break-even point, i.e. costs=sales, anything above this would be profit.; HTH.