One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by 2 times the second number, the result is 11. Use the substitution method. What is the first number?
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dividing the brackets by
To both sides, add 5.
Split each side in half.
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Let the first number be ( x ) and the second number be ( y ).
Given:
 ( x = 3y  4 )
 ( 2x + 3 = 2y + 11 )
Using the substitution method:
Substitute the expression for ( x ) from the first equation into the second equation:
[ 2(3y  4) + 3 = 2y + 11 ]
[ 6y  8 + 3 = 2y + 11 ]
[ 6y  5 = 2y + 11 ]
Subtract ( 2y ) from both sides:
[ 6y  2y  5 = 11 ]
[ 4y  5 = 11 ]
Add 5 to both sides:
[ 4y = 16 ]
Divide both sides by 4:
[ y = 4 ]
Now, substitute the value of ( y ) into the first equation to find ( x ):
[ x = 3(4)  4 ]
[ x = 12  4 ]
[ x = 8 ]
Therefore, the first number is ( x = 8 ).
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Let's denote the first number as ( x ) and the second number as ( y ).
From the given information, we can set up two equations based on the problem statement:

The first number is 4 less than 3 times the second number: [ x = 3y  4 ]

3 more than two times the first number decreased by 2 times the second number equals 11: [ 2x + 3  2y = 11 ]
Now, we can substitute the expression for ( x ) from the first equation into the second equation:
[ 2(3y  4) + 3  2y = 11 ]
Simplify the equation:
[ 6y  8 + 3  2y = 11 ] [ 4y  5 = 11 ]
Add 5 to both sides:
[ 4y = 16 ]
Divide both sides by 4:
[ y = 4 ]
Now, we can substitute the value of ( y ) into the first equation to find ( x ):
[ x = 3(4)  4 ] [ x = 12  4 ] [ x = 8 ]
So, the first number is 8.
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