solve by elimination method

Question

 10.  -4x + 2y = 8                         11.  3a + b = 5                            12.  2m - 5n = -6
    4x - 3y = -10                               2a + b = 10                                   2m - 7n = -14

Answer 1

Elimination method

10)Given equations are  -4x+2y = 8 ---> (1)

4x-3y = -10 ---> (2)

To eliminate the x value add the equations (1)&(2).

-4x+2y = 8

4x-3y = -10

__________

-y = -2

Multiple to each side by negitive one.

y = 2

Substitute the y value in (1).

-4x+4 = 8

Subtract 4 from each side.

-4x+4-4= 8-4

-4x = 4

Divide to each side by negitive 4.

-4x/-4 = 4/-4

x = -1

Solution x = -1,y = 2

11) Given equations are 3a+b = 5 ---> (1)

2a+b = 10 ---> (2)

To eliminate the b value subtract (2) from (1).

3a+b = 5

2a+b = 10

(-) (-)   (-)

_________

a = -5

Substitute the a value in (1).

-15+b = 5

Add 15 to each side.

-15+15+b = 5+15

b = 20

Solution a = -5, b = 20.

 12) Given equations are 2m-5n = -6 ---> (1)

2m-7n = -14 ---> (2)

To eliminate the m value subtract (2) from (1).

2m-5n = -6

2m-7n = -14

(-)  (+)    (+)

___________

2n = 8

Divide to each side by 2.

2n/2 = 8/2

n = 4

Substitute the n value in (1).

2m-20 = -6

Add 20 to each side.

2m-20+20 = -6+20

2m = 14

Divide to each side by 2.

2m/2 = 14/2

m = 7

Solution m = 7, n = 4.