four times one number minus a second is 11, and the sum of the numbers is 14. Find the numbers.
LET 1 NO. BE X,2 NO. BE Y. A|Q 4X-Y=11 X+Y=14 BY SOLVING THESE EQ. X=5, 5+Y=14 SO,Y=9.
To find the numbers, we can set up a system of equations based on the given information.
Let's assume the first number is represented by x, and the second number is represented by y.
According to the first condition, "four times one number minus a second is 11," we can write the equation:
4x - y = 11 ...(Equation 1)
According to the second condition, "the sum of the numbers is 14," we can write the equation:
x + y = 14 ...(Equation 2)
We now have a system of equations with two variables (x and y). We can solve this system of equations to find the values of x and y.
One way to solve this system of equations is through the method of elimination. Here's how:
Step 1: Multiply Equation 2 by 4 to eliminate the variable y:
4(x + y) = 4(14)
4x + 4y = 56 ...(Equation 3)
Step 2: Add Equation 1 and Equation 3 together, eliminating the variable x:
(4x - y) + (4x + 4y) = 11 + 56
8x + 3y = 67 ...(Equation 4)
Step 3: Multiply Equation 2 by 3 to eliminate the variable x:
3(x + y) = 3(14)
3x + 3y = 42 ...(Equation 5)
Step 4: Subtract Equation 5 from Equation 4, eliminating the variable y:
(8x + 3y) - (3x + 3y) = 67 - 42
5x = 25
Step 5: Divide both sides of the equation by 5:
5x/5 = 25/5
x = 5
Now, substitute the value of x back into Equation 2 to solve for y:
5 + y = 14
y = 14 - 5
y = 9
Therefore, the first number (x) is 5, and the second number (y) is 9.