SOLUTION: 2x+3y=35 5x+4y=7 please solve please thank you!

Algebra ->  Equations -> SOLUTION: 2x+3y=35 5x+4y=7 please solve please thank you!      Log On


   

Question 177885: 2x+3y=35
5x+4y=7


please solve please thank you!
Found 3 solutions by oyakhilome, jojo14344, madhan_math:
Answer by oyakhilome(1) About Me  (Show Source):
You can put this solution on YOUR website!
2x+3y=35
5x+4y=7

10x+15y=175
10x+8y =14
------------------
0 +5y=161
y=32.2
5x+4(32.2)=7
5x=121.8
x=24.4

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

Line Eqn's:
2x%2B3y=35, EQN 1
5x%2B4y=7, EQN 2---->y=%28-5x%2B7%29%2F4=-%285%2F4%29x%2B%287%2F4%29, EQN 3
In EQN 1 we get,
3y=35-2x---->cross%283%29y%2Fcross%283%29=%2835-2x%29%2F3
y=-%282%2F3%29x%2B%2835%2F3%29, EQN 4, subst. in EQN 2:
5x%2B4%28%28-2%2F3%29x%2B%2835%2F3%29%29=7
5x-%288%2F3%29x%2B%28140%2F3%29=7
%2815x-8x%29%2F3=7-%28140%2F3%29
7x%2F3=%287-140%29%2F3=%2821-140%2F3%29
7x%2F3=-119%2F3---->7x=cross%283%29%2A%28-119%2Fcross%283%29%29
cross%287%29x%2Fcross%287%29=cross%28-119%2917%2Fcross%287%29
highlight%28x=-17%29 subt. in EQN 3 or EQN 4:
We use EQN 3:
y=-%282%2F3%29%28-17%29%2B%2835%2F3%29
y=34%2F3%2B%2835%2F3%29=highlight%2869%2F3=23%29
We see the graph:
----> RED Line, EQN 1; GREEN Line EQN 2
Thank you,
Jojo



Answer by madhan_math(34) About Me  (Show Source):
You can put this solution on YOUR website!
2x+3y=35
5x+4y=7
Ans:
Given equations are 2x+3y=35-------(1)
5x+4y=7 -------(2)

Equation (1)mutliplied with 4 and equation (2) mutliplied with 3.
(Since if mutliply with these numbers we get the coefficient of y term as same and we neglect y to find the x value easily)

(1) becomes, 8x + 12y = 140-----(3)
15x + 12y = 21-----(4)
Now we subtract equation (3)with (4),We have

-7x = 119
This implies,
-x = 119/7
= 17

Therefore, x = -17 -------(*)
Now we substitute this x value in any of the given equations.

2(-17)+3y = 35
-34 + 3y = 35
3y = 69 ( 35+34)
y = 23 ------ (**)
(*) and (**) are the solutions.

i.e., x = -17
y = 23 (If u like the check the answer is correct,
sub. this x and y values in any of the
given equation you will get equality.)