solve the system of simeltaneous equations :
2x+6y=15 ; 5x-8y=7 detailed answer is needed plz

Question

solve the system of simeltaneous equations :  
2x+6y=15 ;  5x-8y=7     detailed answer is needed plz

anonymous · Answer

okay these two equations are said to be "solved simultaneously" that means that if you solve for x or y in one equation you can "plug it into the other equation"
when you plug the x or y into the other equation you get what the y or x equals. 

in other words if you have two "unknows" you must have atleast two equations to solve for either variable.

here the two unkowns are x and y

anonymous · Answer

to find out exactly what x and y equal you must solve these equations "simultaneously" or in other words together

anonymous · Answer

To start i have the two equations 2x+6y=15 and 5x-8y=7

you can solve either equation for either variable

so randomly ill pick the first equation and ill solve that first one FOR x

so 2x+6y=15    ====>    x = 15/2 - 3y

anonymous · Answer

so i can rewrite what i have now 

5x  - 8y = 7

and 

x = 15/2 -3y

anonymous · Answer

from right above if you SEE that x = 15/2 - 3y AND that the top equation has an x in it. 

you can replace any x 
WITH 15/2 - 3y

because x = 15/2 - 3y

that is because we chose to solve for x

anonymous · Answer

so replacing the x(s) with 15/2 - 3y looks like this

5x - 8y = 7

==>  5 (15/2 - 3y) - 8y = 7

Take a step back and look at what happend we no have an equation that has ONLY y in it. and you can solve for exactly what y is.

solving for y 

==> 75/2 - 15y = 7
then 
==> y = 61/30

anonymous · Answer

no we have exactly what y equals that is 61/30

and we can plug this value into either of the original equations 

so ill plug it into the first equation 2x+6y=15

looks like

2x+6(61/30) = 15 
so 
==> x = 7/5

anonymous · Answer

solving equations simultaneously is this same exact thing for every simultaneous equations problem. so just repeat the major steps over and over for every different problem

steps:
1 pick which equation to solve and variable to solve for and solve
2 plug into other equation
3 solve for the remaining variable 
4 plug the value of the variable into either equation
5 solve for the value of the other variable

anonymous · Answer

Hey thanks very much ..

anonymous · Answer

Perhaps more straightforward, multiply one of the equations so that the coefficient of x (or y) is the same eg multiply the first equation by 5/2 to get 5x +15y = 75/2.

Then subtract the new equation from the second one and the x's will disappear and give you y, then substitute y back in to get x.