Question

The difference of two numbers is 5.The sum of 3 times of one number and 4 times of the other number is 1. Find the numbers.
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Answer 1

Answer:

QUESTION: DETERMINE THE TWO NUMBERS.

Let X = the 1st number

Let Y = the 2nd number

X - Y = 5 (The DIFFERENCE of the two numbers is 5.)

3X + 4Y = 1 (The SUM of 3 TIMES one number and 4 TIMES the OTHER IS 1.

Using the TOP EQUATION(X - Y = 5), solve for X.

X - Y = 5

X - Y + Y = 5 + Y (Add Y to both sides of the equation.)

X = 5 + Y

Now substitute 5 + Y into the BOTTOM EQUATION(3X + 4Y = 1) for X.

3X + 4Y = 1

3(5 + Y) + 4Y = 1 (Substitute 5 + Y for X.)

15 + 3y + 4Y = 1 (Multiply 3 times 5 and 3 times Y. DISTRIBUTIVE PROPERTY)

15 + 7Y = 1 (Combining the Y's (LIKE TERMS).)

15 - 15 + 7Y = 1 - 15 (Subtract 15 from both sides.)

7Y = - 14

7Y/7 = -14/7 (Divide both sides by 7.)

Y = -2

SO, Y = -2

NEXT, DETERMINE THE VALUE OF Y BY SUBSTITUTING THE VALUE OF Y(-2)

IN THE TOP EQUATION X - Y = 5.

X - (-2) = 5 (Substituting value of Y(-2) into equation.)

X + 2 = 5

X + 2 - 2 = 5 -2 (Subtract 2 from both sides.)

X = 3

S, X = 3

CHECKING:

Use the the TOP EQUATION: DOES X - Y = 5?

X - Y = 3 - (-2) = 3 + 2 = 5 YES!

Use the BOTTOM EQUATION: DOES 3X + 4Y = 1?

3(3) + 4(-2) = 9 - 8 = 1 YES!

ALSO, these two equations are LINEAR. They represent STRAIGHT LINES, and

these two lines INTERSECT each other at (3,-2)