Algebra II word problem?

Question

The sum of two numbers is 34. Their difference is 8. Find the two numbers by writing a system of equations. Solve using linear combinations.

 

Answer 1

Let x and y be the two numbers.

The word " The sum of two numbers x and y is 34 " represent the equation x + y = 34.

The word " The difference of two numbers x and y is 8 " represent the equation x - y = 8.

 

Substitution Method :

The system of equations are x + y = 34 and x - y = 8.

Step 1 : Solve the either equation for x or y since the coefficient is 1 or negative 1.

Solve the equation 2 : x - y = 8 for x.

Add y to each side.

x - y + y = 8 + y

x = 8 + y

Step 2 : Substitute 8 + y for x in the equation 1 : x + y = 34 to find the value of y.

(8 + y) + y = 34

8 + 2y = 34

Subtract 8 from each side.

8 + 2y - 8 = 34 - 8

2y = 26

Multiply each side by 2.

y = 13.

 

Step 3 : Substitute 13 for y in either equation to find x.

Equation 2 : x - y = 8.

x - (13) = 8

Add 13 to each side.

x - 13 + 13 = 8 + 13

x = 21.

 

The solution is (21, 13).