Question

Use elimination (adding or subtracting) to find the common solution

Answer 1

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).