Question

Look at this system of equations. 4x+3y=33 2x+3y=21 What is the value of x+y?

Answer 1

Answer:

x = 6

y = 3

x + y = 9

Step-by-step explanation:

(Step 1)

Isolate one of the variables in one of the equations. This will allow you to solve by substitution in the following steps.

2x + 3y = 21                             <----- Original equation

3y = -2x + 21                            <----- Subtract 2x from both sides

y = (-2/3)x + 7                          <----- Divide all terms by 3

(Step 2)

Substitute the new equation into the untouched equation and isolate the "x" variable.

4x + 3y = 33                                 <----- Original equation

4x + 3((-2/3)x + 7) = 33                <------ Substitute manipulated equation

4x - 2x + 21 = 33                          <------ Multiply 3 by terms in parentheses

2x + 21 = 33                                 <------ Subtract terms with variables

2x = 12                                         <----- Subtract 21 from both sides

x = 6                                             <----- Divide both sides by 2

(Step 3)

Plug the value of "x" into one of the equations to find the value of "y".

4x + 3y = 33                               <----- Original equation

4(6) + 3y = 33                             <----- Plug 6 in for "x"

24 + 3y = 33                               <----- Multiply

3y = 9                                         <----- Subtract 24 from both sides

y = 3                                           <----- Divide both sides by 3

(Step 4)

Since you now know the value of both variables, you can add them together to find your final answer.

x = 6

y = 3

x + y = ?

6 + 3 = ?

9 = ?