By the elimination method the solution for equations 6x-3y=21 and -3x+2y=5 are x = 19 and y = 31.
Step-by-step explanation:
The given is,
[tex]6x-3y=21[/tex]......................................(1)
[tex]-3x+2y=5[/tex]........................................(2)
Step:1
By elimination method,
Multiplying the equation (1) by 2 ( Eqn(1) × 2 )
[tex]12x-6y=42[/tex]..............................(3)
Multiplying the equation (2) by -3 ( Eqn(2) × -3)
[tex]9x-6y=-15[/tex]..............................(4)
Step:3
Subtracting the equations (3) and (4)
[tex]12x-6y=42[/tex]
[tex]9x-6y=-15[/tex]
( - )
( [tex]12x-9x[/tex] ) + ( [tex]-6y + 6y[/tex] ) = ( [tex]42 +15[/tex] )
( [tex]3x[/tex] ) = 57
[tex]x = 19[/tex]
Step:4
Substitute the x value in Eqn (1),
[tex]6x-3y=21[/tex]
( 6 × 19 ) - ( [tex]3y[/tex] ) = 21
- [tex]3y[/tex] = -93
[tex]y = 31[/tex]
Step:5
Check for solution,
Substitute the values of x and y in Equation (1),
[tex]6x-3y=21[/tex]
( 6 × 19 ) - ( 3 × 31 ) = 21
21 = 21
Result:
The solution for equations 6x-3y=21 and -3x+2y=5 are x = 19 and y = 31.
