Three times the smaller of two consecutive odd integers is the same as 116 less than 5 times the larger integer find the integer
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2. 3x - 5y = -2
x + 3y = 4
Let us multiply equation 2 by three, so we can use the elimination method.
3x + 9y = 12
Now, let us subtract equation 1 from equation 2.
3x + 9y - 3x + 5y = 12 + 2
14y = 14
y = 1
Let us substitute this value of y in equation 2.
x + 3(1) = 4
x = 4 - 3
x = 1
3. -3x + 3y = -6
6x + 4y = 42
Let us multiply equation 1 by 2, so we can use the elimination method.
-6x + 6y = -12
Let us now add equations 1 and 2, so as to eliminate x.
6x + 4y -6x + 6y = 42 - 12
10y = 30
y = 3
Let us now substitute this value of y in equation 1, so as to find x.
-3x + 3(3) = -6
-3x + 9 = -6
-3x = -15
3x = 15
x = 5
4. 12x + 4y = 20
2x - 2y = -2
Let us multiply equation 2 by 2, so as to use the elimination method.
4x - 4y = -4
Let us now add equations 1 and 2, so as to eliminate y.
4x - 4y + 12x + 4y = -2 + 20
16x = 18
x = =
= 1.125
Let us substitute this value of x in equation 2, so as to find y.
2(9/8) -2y = -2
9/4 - 2y = -2
-2y = -2 - 9/4
2y = 17/4
y = = 2.125