Question

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

3x-8y=7    x+2y=-7

Answer:
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Answer 1

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

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 = -
`(21)/(7)` = - 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 =
`(- 16)/( 8)` = - 2

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