# How do you solve the following system?: #y=2x-3 , 5x + 3y = -3 #

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To solve the system of equations ( y = 2x - 3 ) and ( 5x + 3y = -3 ), you can use the substitution method or the elimination method.

First, solve the first equation for ( y ) in terms of ( x ): ( y = 2x - 3 ).

Then, substitute ( 2x - 3 ) for ( y ) in the second equation: ( 5x + 3(2x - 3) = -3 ).

Now, solve for ( x ):

( 5x + 6x - 9 = -3 )

( 11x - 9 = -3 )

( 11x = 6 )

( x = \frac{6}{11} )

Next, substitute the value of ( x ) back into either of the original equations to solve for ( y ). Using the first equation is usually simpler:

( y = 2(\frac{6}{11}) - 3 )

( y = \frac{12}{11} - 3 )

( y = \frac{12}{11} - \frac{33}{11} )

( y = \frac{-21}{11} )

So, the solution to the system of equations is ( x = \frac{6}{11} ) and ( y = \frac{-21}{11} ).

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