Respuesta :
The solution for the given equations [tex]2x-5y=-5[/tex] and [tex]x+y=8[/tex] are (x, y) respectively (5, 3).
Step-by-step explanation:
The given is,
[tex]2x-5y=-5[/tex].................................................(1)
[tex]x+y=8[/tex]........................................................(2)
Step:1
By using the elimination method for the above equations are,
Multiply the equation (2) by 2 ( Eqn(2) × 2)
[tex]2x+2y=16[/tex].............................................(3)
Step:2
Subtract the Equation (1) and (3),
[tex]2x-5y=-5[/tex]
[tex]2x+2y=16[/tex]
( - )
( [tex]2x[/tex] - [tex]2x[/tex] ) + ( [tex]-5y[/tex] - [tex]2y[/tex] ) = ( [tex]-5[/tex] - [tex]16[/tex] )
[tex]-7y[/tex] = [tex]-21[/tex]
[tex]y[/tex] = 3
Step:3
Substitute the value of y in Eqn (2),
[tex]x+y=8[/tex] ............................(2)
[tex]x+3=8[/tex]
[tex]x=8-3[/tex]
[tex]x=5[/tex]
Step:4
Check for solution,
Substitute the x and y values in Eqn (1),
[tex]2x-5y=-5[/tex] ........................(1)
(2 × 5) - (5 × 3) = -5
10 - 15 = -5
-5 = -5
Result:
The solution for the equations [tex]2x-5y=-5[/tex] and [tex]x+y=8[/tex] are (x, y) respectively (5, 3).
