solve equations!!!!!!!!!!!!!!!!!!!

Question

7) -4x+y=6

    -5x-y=21

8) -7x-2y=-13

     x-2y=11

9) -5x+y=2

    -3x+6y=-12?

Answer 1

Contd.......

• 9).

Substitution Method :

The system of equations are - 5x + y = 2 and - 3x + 6y = - 12.

Step 1 :

Simplify equation 1 : - 5x + y = 2.

- 5x + y = 2.

Add 5x to each side.

y = 2 + 5x.

Equation 2 : - 3x + 6y = - 12.

Divide each side by negative 3.

x - 2y = 4 → (3).

Step 2 : To find the value of x,substitute 2 + 5x for y in the equation 3 : x - 2y = 4.

x - 2(2 + 5x) = 4

x - 4 - 10x = 4

- 9x = 4 + 4 = 8

Divide each side by negative 9.

x = - 8/9.

 

Step 3 : To find the value of y, substitute x = - 8/9 in either of the equations.

Equation 1 : - 5x + y = 2

- 5(- 8/9) + y = 2

40/9 + y = 2

y = 2 - 40/9

y = (18 - 40)/9

y = - 22/9.

 

The solution is (x, y) = (- 8/9, - 22/9).

Answer 2

• 7).

Substitution Method :

The system of equations are - 4x + y = 6 and - 5x - y = 21.

Step 1 : Simplify equation 2.

- 5x - y = 21.

Add 5x to each side.

- y = 21 + 5x

Multiply each side by negative.

y = - 5x - 21.

Step 2 : To find the value of x, substitute y = - 5x - 21 in the equation 1.

- 4x + (- 5x - 21) = 6

- 4x - 5x = 6 + 21

- 9x = 27

Divide each side by negative 9.

x = - 27/9

x = - 3.

Step 3 : To find the value of y, substitute x = - 3 in either of the equations.

Equation 1 : - 4x + y = 6

- 4(- 3) + y = 6

12 + y = 6

y = 6 - 12 = - 6.

The solution is (x, y) = (- 3, - 6).

• 8).

Elimination Method :

The system of equations are : - 7x - 2y = - 13 → (1)

                                               x - 2y = 11 → (2).

Step 1 : Since, the coeffient of y is same(i.e, - 2), write the equations (1) and (2) in column form, then subtract them each other, to find the value of x.

- 7x - 2y = - 13

x - 2y = 11

( - ) ___________

- 8x = - 24

Divide each side by negative 8.

x = 3.

Step 2 : Substitute 3 for x in either equation to find y.

Equation 2 : x - 2y = 11.

(3) - 2y = 11

2y = 3 - 11

2y = - 8

y = - 8/2

y = - 4.

The solution is (x, y) = (3, - 4).