Question

pls solve this sum for me
simultaneous equations.
9/x+y + 5/x-y = 8
12/x+y + 7/x-y = 11.​

Answer 1

Up to now we have solved equations with only one unknown variable. When solving for two unknown variables, two equations are required and these equations are known as simultaneous equations. The solutions are the values of the unknown variables which satisfy both equations simultaneously. In general, if there are n unknown variables, then n independent equations are required to obtain a value for each of the n variables.

An example of a system of simultaneous equations is:

x+y =−1 3 =y−2x

We have two independent equations to solve for two unknown variables. We can solve simultaneous equations algebraically using substitution and elimination methods. We will also show that a system of simultaneous equations can be solved graphically.

Solving by substitution (EMA39)

Use the simplest of the two given equations to express one of the variables in terms of the other.

Substitute into the second equation. By doing this we reduce the number of equations and the number of variables by one.

We now have one equation with one unknown variable which can be solved.

Use the solution to substitute back into the first equation to find the value of the other unknown variable.

The following video shows how to solve simultaneous equations using substitution.

Video: 2FD5

WORKED EXAMPLE 6: SIMULTANEOUS EQUATIONS

Solve for x and y:

x−y =1…(1) 3 =y−2x…(2)

Use equation (1) to express x in terms of y

x=y+1

Substitute x into equation (2) and solve for y

3 =y−2(y+1) 3 =y−2y−2 5 =−y ∴y =−5

Substitute y back into equation (1) and solve for x

x =(−5)+1 ∴x =−4

Check the solution by substituting the answers back into both original equations

Write the final answer

x =−4 y =−5

WORKED EXAMPLE 7: SIMULTANEOUS EQUATIONS

Solve the following system of equations:

Answer 2

Answer:

1/x+y= 3 , 1/x-y = 1

Step-by-step explanation:

lets take 1/x+y as u and 1/x-y as v

now the equations becomes :

9u + 5v = 8 --------------(1)

12u + 7v = 11 -------------(2)

Multiply these two equations so that one of the constant will be similar and you can cancel them .

(9u + 5v = 8) × 7 ---------(1)

(12u + 7v = 11) × 5 -------(2)

On multiplying :

63u + 35v = 56 -------(3)( subtract the two equation)( + 35 and - 35 cancel

each other )              

60u + 35v = 55 -------(4)

3u = 1

u = 1/3

Imply u =1/3 in the first equation :

9u + 5v = 8

9 × 1/3 + 5v = 8

3 + 5v = 8

5v = 8 - 3

5v = 5

v = 1

1/x+y = u , u = 1/3

we have to take the reciprocal of the fraction 1/3 . therefore it becomes 3 .

hence 1/x+y = 3

hence 1/x-y = 1

hope it helps

have a wonderful day :)