Use the linear combination method to solve the system of equations. explain each step of your solution.

3x-8y=7    x+2y=-7

The value of x is - 3  And The value of y = - 2

Step-by-step explanation:

Given equation as :

3 x - 8 y = 7          ......A

x + 2 y = - 7          ......B

Applying Linear combination method :

A linear combination method in which steps are taken to make both equation coefficient as like terms to get the value of variable .

Step 1

multiply the equation B with 4

I,e 4 × ( x+ 2 y ) = - 7 × 4

or, 4 x + 8 y = - 28       ......C

Step 2

Arrange  equation A and C in column

So , 3 x - 8 y = 7          .

      4 x + 8 y = - 28

Step 3

Add Eq 3 with Eq 1

I.e (   4 x + 8 y ) + (  3 x - 8 y ) = 7 - 28

Or. ( 4 x + 3 x ) + ( 8 y - 8 y ) = - 21

Or,  7 x + 0 = - 21

∴     x =  - = - 3

Put the value of x in eq A ,  to get the value of y

So , 3 × ( - 3 ) - 8 y = 7

Or,  - 9 - 8 y = 7

Or, 8 y = - 9 - 7 = - 16

∴     y =   = - 2

Hence The value of x is - 3  And The value of y = - 2   Answer

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.