the solution of the system of linear equation 300x+200y=500 and 7x-5y=31 is;?

Question

the solution of the system of linear equation 300x+200y=500 and 7x-5y=31 is;
a) (x,y)=(-2,3)
b) (x,y)=(3,-2)
c) (x,y)=(2,-3)
d) (x,y)=(-3,2)
e) non of these.

Answer 1

(b).

Multiply the second equation by 40 (to get -200y in it):

300x+200y=500
280x-200y=1240

Add the two equations and the "y" terms cancel out:

300x+200y=500
280x-200y=1240
=============
580x = 1740

580x/580 = 1740/580
x = 3

Go back to one of the origination equations:

7x - 5y = 31
7*3 - 5y = 31
-5y = 10
y = -2

The answer is (3,-2).

Answer 2

300x+200y=500 divide by 100
3 x + 2 y = 5 (1) and 7x-5y=31 ( 2 )

multiply ( 1 ) by 5 snd ( 2 ) by 2

15 x + 10 y = 25 and 14 x - 10 y = 62

add the two equation

29x = 87 divide by 29

x = 3 substitute in ( 1 )

9 + 2y = 5

2y = 5 - 9

2y = - 4 divde by 2

y = - 2
the solution is :
b) (x,y)=(3,-2)

Answer 3

300x+200y = 500
7x-5y=31
1.) Multiply 2nd equation by 40

300x + 200y = 500
40(7x-5y=31) = 280x-200y = 1240

2.) Combine like terms.

580x = 1740

3.) Solve for x
580x/580 = 1740/580
x=3

4.) Substitute and solve for y
7(3)-5y = 31
21-5y = 31
-5y = 10
y= -2

Solution: (3,-2) (b)

5.) Check:
300(3)+200(-2) = 500
900 -400 = 500
500 = 500 Yes

Answer 4

it is how my math instructor taught it: 7x-3y=3 x=2y+2 plug in 2y+2 everywhere you notice an x. 7(2y+2)-3y=3 use the distributive assets 7 cases 2y=14y 7 cases 2=14 14y+14-3y=3 14y-3y=11y 11y-14=3 upload 14 to the two factors 11y=-11 divide the two factors via 11 y=-a million plug in destructive a million to between the 1st equations. i choose x=2y+2 x=2(-a million)+2 2 cases -a million=-2 -2+2 cancel one yet another out x=0 write the respond like this {0,-a million}

Answer 5

you'd better simplify the 1st with 100 and this way you get 3x+2y=5 and you should make a sistem with the other ecuation.
3x+2y=5 /*5 =>15x+10y=25
7x-5y=31 /*2 =>14x-10y=62 then you sum the both ecuations and you get 29x=87=>x=3
then you replace x in one ecuation and this way u find y
y=(5-9)/2=-2
So,the sollution is a) (x,y)=(-2,3)

Answer 6

b) (3,-2)
first simplify que by dividing 1 eq by 100 i.e. 3x+2y=5
now by comparing coefficients method,
mul 1 eq by 7 i.e 21x+14y=35
mul 2 eq by 3 i.e. 21x-15y=31
sub both eq to get 29y=-58
y=-2
put value of y in eq 1 i.e. x=3