Question

solve the pair of leainer equations x +y-7=0;5x+12y-7=0

Answer 1

x + y - 7 = 0

=> x + y = 7 ..........(A)

Multiplying the above equation by 5,

5x + 5y = 35 ..........(1)

5x + 12y - 7 = 0

=> 5x + 12y = 7 ........(2)

Subtraction equation (1) from (2)

5x + 12y = 7

-5x - 5y = -35

----------------------

7y = -28

----------------------

Thus, y = -4

Putting the value of y in equation (A)

x - 4 = 7

=> x = 11

Answer 2

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

We have given two Equation :x+y=7

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \:$5x+12y=7

The above equation can be solved by elimination method:

x+y=7----(×5)

5x+12y=7------(×1)

New Equation obtained:-5x+5y=35

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$5x+12y=7

=>5x+5y=35

=>5x+12y=7

$\:(-)\:(-)\:\:(-)$

____________

-7y=-28

y=4

Now,put y's value into this equation:

x+y=7

=>x+4=7

=>x=7-4=3

x=3

∴X=3 & y=4

Extra information=>

Elimination method is a way of eliminating one variable from equation of two variable so that we can find value of one variable.

Elimination means =>To Remove

Method step by step For Elimination Method :

step 1: Firstly Multiply with any non-zero value so that the coefficient of any one variable be equal and gets eliminated.

Generally we multiply with coefficient of a variable of both equation to each term.

step2: After Put negative sign where value is positive and put positive sign where value is negative so that any one variable gets eliminated or subtracted and hence we find value of any one variable.

step3: Now,after finding value of one variable substitute it another equation.