By using elimination method the solution for the given equations 5x+6y=17 and -10x-9y= -43 are x=7 and y= -3.
Step-by-step explanation:
The given equations are,
[tex]5x+6y=17[/tex]..................................(1)
[tex]-10x-9y=-43[/tex]..............................(2)
Step:1
By elimination method,
Multiplying the equation (1) by 9 ( Eqn (1) × 9)
[tex]45x+54y=153[/tex].................................(3)
Multiplying the equation (2) by -6 ( Eqn (2) × -6)
[tex]60x+54y=258[/tex]................................(4)
Step:2
Subtracting the Equations (3) and (4),
[tex]45x+54y=153[/tex]
[tex]60x+54y=258[/tex]
( - )
( [tex]45x-60x[/tex] ) + ( [tex]54y-54y[/tex] ) = ( [tex]153-258[/tex] )
( [tex]-15x[/tex] ) = ( [tex]-105[/tex] )
[tex]x = 7[/tex]
Step:3
Substitute the x=7 in equation (1),
[tex]5x+6y=17[/tex]
( 5 × 7 ) + ( [tex]6y[/tex] ) = 17
[tex]6y[/tex] = -18
[tex]y[/tex] = -3
Step:4
Check for solution,
Substitute the x and y values in Eqn (1),
[tex]5x+6y=17[/tex]
( 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.
