Question

Solve the simultaneous equations. You must show all your working to find x and y. 1/2x -3y = 9 5x y + y = 28

Answer 1

1/2x - 3y = 9 (1)
5x + y = 28 (2)

(1) x 2
x - 6y = 18

(2) x 6
30x + 6y = 168
—————

x - 6y = 18 (3)
30x + 6y = 168 (4)

(3) + (4)
31x = 186
x = 6

sub x into (2)
30 + y = 28
y = -2
—————

x = 6
y = -2

Answer 2

`\huge\boxed{x = 6 , y = -2}`

Explanation:

`\sf (1)/(2) x - 3y = 9-----------(1)\\5x + y = 28 ----------(2)`

Taking equation (1)

`\sf (1)/(2) x -3 y=9`

Multiplying both sides by 2

`\sf x-6y = 18`

Adding 6y to both sides

`\sf x = 18+6y`

Putting this in (2)

5(18+6y) + y = 28

5(18+6y) + y = 28

90 + 30y+y = 28

31y+90-28 = 0

31 y + 62 = 0

31y = -62

Dividing both sides by 31

y = -2

Now,

x = 18 + 6y

x = 18+6(-2)

x = 18-12

x = 6