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# 2x-3y=9 -5x-3y=30

I need to find both x and y and tehy need to be the same in both problems. The topic is Elimination Using Addition and Subtraction to solve Systems.

You have a system of linear equations for which you need to solve for; that is, you need to solve for the unknown variables, x and y. To solve for the system using the elimination method, you will need to multiply one or both equations, if necessary, by a constant in such a way that will eliminate one of the variables when the equations are added to one another so that you can solve for the other variable. Once you've solved for one of these variables, you can solve for the other variable that you initially eliminated by plugging in the value of the variable you already solved for into one of the original equations.

2x - 3y = 9

-5x - 3y = 30

For simplicity, let's eliminate the y variable in this system by multiplying the second equation by -1:

-1·(-5x - 3y = 30)

==>   -1·-5x  -  -1·3y  =  -1·30

==>   5x + 3y = -30

Add this equation to the first original equation:

2x   -  3y  = 9

+   5x  +  3y  =  -30

__________________

2x + 5x - 3y + 3y = 9 + -30     ==>     7x  +  0y  =  -21     ==>     7x  =  -21

7x  =  -21

7x/7  =  -21/7     ==>     x = -3

Plug this value for x into either of the original equations from the system (I will use the first equation) to solve for y:

2x - 3y = 9

2·(-3)  -  3y  =  9

-6  -  3y  =  9

Add 6 to both sides of the equation:

-6  +  6  -  3y  =  9  +  6

-3y  =  15

Divide both sides of the equation by -3:

-3y/-3  =  15/-3

y = -5