A) The solution (x,y) is (9,-2).
B) The solution (x,y) is (6, -1/2).
C) The solution (x,y) is (-5,2).
D) The solution (x,y) is (1, -10).
Step-by-step explanation:
A) x+y=7 and x+2y=5
Subtract the second equation from the first equation.
x+y = 7
-(x+2y = 5)
-y = 2
⇒ y = -2
The value of y is -2.
Substitute y= -2 in any of the equation.
⇒ x + (-2) = 7
⇒ x = 7+2
⇒ x = 9
The value of x is 9.
The solution (x,y) is (9,-2).
B) x+2y=5 and x-2y=7
Add both the equations.
x + 2y = 5
x - 2y = 7
2x = 12
⇒ x = 12/2
⇒ x = 6
The value of x is 6.
Substitute x= 6 in any of the equations.
⇒ 6 + 2y = 5
⇒ 2y = 5-6
⇒ 2y = -1
⇒ y = -1/2
The value of y is -1/2.
The solution (x,y) is (6, -1/2).
C) x+4y=3 and -x+y=7
Add both the equations.
x + 4y = 3
-x + y = 7
5y = 10
⇒ y = 10/5
⇒ y = 2
The value of y is 2.
Substitute y=2 in any of the equations.
⇒ -x + 2 = 7
⇒ -x = 7-2
⇒ -x = 5
⇒ x = -5
The value of x is -5.
The solution (x,y) is (-5,2).
D) 5x-2y=25 and 4x-2y=24
Subtract the second equation from the first equation.
5x - 2y = 25
- (4x - 2y = 24)
x = 1
The value of x is 1.
Substitute x=1 in any of the equations.
⇒ 5(1) - 2y = 25
⇒ 5 -2y = 25
⇒ -2y = 25-5
⇒ -2y = 20
⇒ y = -20/2
⇒ y = -10.
The value of y is -10.
The solution (x,y) is (1, -10).
