Question

Solve the system using elimination. 2x-5y=-5 x+y=8

Answer 1

The solution for the given equations
`2x-5y=-5` and
`x+y=8` are (x, y) respectively (5, 3).

Explanation:

The given is,

`2x-5y=-5`.................................................(1)

`x+y=8`........................................................(2)

Step:1

By using the elimination method for the above equations are,

Multiply the equation (2) by 2 ( Eqn(2) × 2)

`2x+2y=16`.............................................(3)

Step:2

Subtract the Equation (1) and (3),

`2x-5y=-5`

`2x+2y=16`

( - )

(
`2x` -
`2x` ) + (
`-5y` -
`2y` ) = (
`-5` -
`16` )

`-7y` =
`-21`

`y` = 3

Step:3

Substitute the value of y in Eqn (2),

`x+y=8` ............................(2)

`x+3=8`

`x=8-3`

`x=5`

Step:4

Check for solution,

Substitute the x and y values in Eqn (1),

`2x-5y=-5` ........................(1)

(2 × 5) - (5 × 3) = -5

10 - 15 = -5

-5 = -5

Result:

The solution for the equations
`2x-5y=-5` and
`x+y=8` are (x, y) respectively (5, 3).