The sum of two numbers is 53. If twice the 1st number minus 3 times the second number is 26, find both numbers.

The sum of three times the number and 14 is 53

26x =9y =w

To find the two numbers, we can set up a system of equations based on the given information. Let's assume the first number is 'x' and the second number is 'y'.

From the first statement, we know that the sum of the two numbers is 53, so we can write the equation:
x + y = 53 (Equation 1)

From the second statement, we are given that twice the first number minus three times the second number is 26, so we can write the equation:
2x - 3y = 26 (Equation 2)

Now we have a system of two equations with two variables. We can solve this system by using either substitution or elimination method. Let's use the elimination method.

Multiply Equation 1 by 3 to make the coefficients of 'y' the same in both equations:
3(x + y) = 3(53)
3x + 3y = 159 (Equation 3)

Now, subtract Equation 2 from Equation 3 to eliminate the variable 'y':
3x + 3y - (2x - 3y) = 159 - 26
3x + 3y - 2x + 3y = 133
x + 6y = 133 (Equation 4)

Now we have a new equation (Equation 4) with the variables 'x' and 'y'. We can solve this equation for 'x'.

Subtract Equation 1 from Equation 4 to eliminate the variable 'x':
x + 6y - (x + y) = 133 - 53
x + 6y - x - y = 80
5y = 80

Divide both sides of the equation by 5:
5y/5 = 80/5
y = 16

Now that we have the value of 'y', we can substitute it back into Equation 1 to find 'x':
x + 16 = 53
x = 53 - 16
x = 37

Therefore, the first number is 37, and the second number is 16.