Question

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Answer 1

Explanation:

1) y = 2x ----------(I)

x + y = 6 -----------(II)

Plug in y =2x in equation (II)

x + 2x = 6 {Add like terms}

3x = 6

x = 6/3

x = 2

Plugin x = 2 in (I)

y = 2*2

y = 4

Check:

LHS = x +y

= 2 + 4

= 6 = RHS

2)5x + 10y = 3 ------------(I)

x = (-1/2) y ------------(II)

Substitute x = (-1/2)y in (I)

`5*(-1)/(2)y + 10y = 3\\\\(-5)/(2)y+ (10*2)/(1*2)y = 3\\\\(-5)/(2)y+(20)/(2)y=3\\\\(-5+20)/(2)y = 3\\\\(15)/(2)y=3\\\\ y = 3*(2)/(15)\\\\ y = (2)/(5)`

Substitute y = (2/5) in equation (II)

`x = (-1)/(2)*(2)/(5)\\\\x = (-1)/(5)`

Check:

Substitute x and y value in equation (I)

`LHS = 5*(-1)/(5)+10*(2)/(5)\\\\ = -1 + 2*2\\\\ = -1 + 4\\ = 3 = RHS`

3) y - x = 3x + 2

y = 3x + 2 + x

y = 4x + 2 ---------------(I)

2x + 2y = 14 - y

2x + 2y +y = 14

2x + 3y = 14 ------------------(II)

Substitute y = 4x + 2 in equation (II)

2x + 3(4x +2) = 14

2x + 3*4x + 3*2 = 14

2x + 12x + 6 = 14

14x + 6 = 14

14x = 14 - 6

14x = 8

x = 8/14

x = 4/7

Substitute 'x' value in (I)

`y = 4*(4)/(7) +2\\\\y = (16)/(7)+2\\\\y= (16)/(7)+(2*7)/(1*7)\\\\y=(16)/(7)+(14)/(7)\\\\y=(30)/(7)`

Check:

`LHS = 2x + 3y\\\\ = 2*(4)/(7)+3*(30)/(7)\\\\ = (8)/(7)+(90)/(7)\\\\=(8+90)/(7)\\\\=(98)/(7)\\\\=14 = RHS`