Question

eight times the smaller of two numbers plus two times the larger number is 44. Three times the smaller number minus two times the larger number is zero. Find the numbers (use the system of equations.)

Answer 1

Simultaneous Equations

The two numbers are 4 and 6

Explanation:

Let the smaller number : x

Let the larger number :y

Hence the equations formed are :

8x + 2y = 44 -----------------------------( 1 )

3x - 2y = 0 -------------------------------( 2 )

Solving Equation (2)

3x = 2y

And substituting the value of 2y from the above the equation in Eqn 1

Hence it becomes

⇒ 8x + 3x =44

⇒ 11x = 44

Thus the value of x is 4

Now putting the value of x in eqn 2 to solve for y

And from it we get the value of y = 6

Hence the the two numbers x and y are x= 4 , y = 6

Answer 2

4 and 6

Explanation:

Let the smaller number be x

The bigger number be y

Eight times the smaller of two numbers plus two times the larger number is 44.

8x+2y=44

Three times the smaller number minus two times the larger number is zero

3x-2y=0

8x+2y=44

3x-2y=0

Using elimination method

Add both sides

8x+3x+2y+(-2y)= 44+0

11x= 44

x=44/11=4

Put x = 4 back in one of the equation

3x-2y=0

3(4)-2y=0

12-2y=0

Add 2y to both sides

12 = 2y

Divide both sides by 2

12/2 =y = 6

The smaller number (x) is 4 and the larger number (y) is 6