SOLUTION: ASAP:plz What is the value of the y variable in the solution to the following system of equations? 5x + 3y = 7 3x - 5y = -23

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Question 601391: ASAP:plz
What is the value of the y variable in the solution to the following system of equations?
5x + 3y = 7
3x - 5y = -23
Found 2 solutions by lawdej, w_parminder:
Answer by lawdej(58)   (Show Source): You can put this solution on YOUR website!
here is the solution
multiply the first equation by 5 and the second equation by 3
25x+15y=35
9x-15y=-69
now add both of them
34x=-34
x=-1
substitute x=-1in one of the equations to get value of y
5x-1+3y=7
-5+3y=7
3y=7+5
3y=12
y=4
so the value of the y variable is 4
Answer by w_parminder(53)   (Show Source): You can put this solution on YOUR website!
There are many methods to solve the system of linear equations, but I use the 'elimination method' most of the times.
In this method, you have to multiply either one or both the equations with an integer in order to make the coefficients of any of the variables in the equations exactly equal to each other. After this, you subtract any of the equation from the other to eliminate that variable.
5x + 3y = 7 (equation I)
3x - 5y = -23 (equation II)
We have to find the value of 'y' only, so I must eliminate 'x' from these equations. To do so, I first find the LCM of the coefficients of 'x' in the equations, i.e. of 5 & 3, which is 15.
Now we multiply equation I with 3 and equation II with 5 to equate the coefficients of 'x'.
Now the equations became
( equation I)*3 => 15x + 9y = 21
(equation II)*5 => 15x - 25y = -115
On Subtracting the new equations, we get
(15x + 9y)-(15x - 25y) = 21 - (-115)
15x + 9y - 15x + 25y = 21 + 115
34y = 136
So y = 136/34 = 4
This is your required answer, but if you want to find the value of 'x', then put this value of 'y' in any of the given equations and solve it. Let's put this value in equation I
So equation I => 5x + 3*(4) = 7
i.e. 5x + 12 = 7
i.e. 5x = 7 - 12
i.e. 5x = -5
i.e. x = -5/5
i.e. x = -1



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