Question

If 4x +3y = 15 and 4x -3y = 9, the value of x + y is

Answer 1

Answer:

Step-by-step explanation:

x=3

y=1

x+y=3+2=5

Answer 2

Answer:

The value of x + y is

$\boxed{x+y=4}$

Step-by-step-explanation:

The given simultaneous equations are

${4x + 3y = 15\:\:\: ... ( 1 )}$

${4x - 3y = 9\:\:\: ... ( 2 )}$

Now, by adding equations ( 1 ) and ( 2 ), we get,

4x + 3y = 15 .... ( 1 )

+ 4x - 3y = 9 ...( 2 )

____________

8x = 24

$\therefore\:x=\frac{24}{8}$

$\therefore\boxed{x=3}$

Now, by substituting x = 3 in equation ( 1 ), we get,

4x + 3y = 15

$\therefore\:4\times3+3y=15\\\\\longrightarrow\:12+3y=15\\\\\longrightarrow\:3y=15-12\\\\\longrightarrow\:3y=3\\\\\longrightarrow\:y=\frac{3}{3}\\\\\therefore\boxed{y=1}$

Now,

x = 3

y = 1

$\therefore\:x+y=3+1=4$

$\boxed{x+y=4}$

Additional Information:

1. Linear Equations in two variables:

The equation with the highest index ( degree ) 1 is called as linear equation. If the equation has two different variables, it is called as 'linear equation in two variables'.

The general formula of linear equation in two variables is

ax + by + c = 0

Where, a, b, c are real numbers and

a ≠ 0, b ≠ 0.

2. Solution of a Linear Equation:

The value of the given variable in the given linear equation is called the solution of the linear equation.

3. Trick to solve problem like x + y and x - y :

In some equations, the coefficient of x is exhnaged to coefficient of y and other one is exchanged to another in both the equations.

In such cases, we use following tricks:

1. Add the both equations.

2. We will get, one more equation which can be reduced to ( x + y ).

3. Subtract the second equation from the first.

4. We will get, one more equation which can be reduced to ( x - y ).

5. Now, solve the two equations ( x + y ) and

( x - y ).

6. Get the solutions of the equations.