Question

What is the solution of the system? Use elimination.
5x + 6y = 17
−10x − 9y = −43

Answer 1

By using elimination method the solution for the given equations 5x+6y=17 and -10x-9y= -43 are x=7 and y= -3.

Explanation:

The given equations are,

`5x+6y=17`..................................(1)

`-10x-9y=-43`..............................(2)

Step:1

By elimination method,

Multiplying the equation (1) by 9 ( Eqn (1) × 9)

`45x+54y=153`.................................(3)

Multiplying the equation (2) by -6 ( Eqn (2) × -6)

`60x+54y=258`................................(4)

Step:2

Subtracting the Equations (3) and (4),

`45x+54y=153`

`60x+54y=258`

( - )

(
`45x-60x` ) + (
`54y-54y` ) = (
`153-258` )

(
`-15x` ) = (
`-105` )

`x = 7`

Step:3

Substitute the x=7 in equation (1),

`5x+6y=17`

( 5 × 7 ) + (
`6y` ) = 17

`6y` = -18

`y` = -3

Step:4

Check for solution,

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

`5x+6y=17`

( 5 × 7 ) + ( 6 × -3 ) = 17

( 35 ) - ( 18 ) = 17

17 = 17

Result:

The solution for the equations 5x+6y=17 and -10x-9y= -43 are x=7 and y= -3.