maths help?

Question

find the co-ordinates of the vertex where they intersect the ;lines are 2x - y = - 9 and x - 2y = -9

Answer 1

2x - y = - 9 ... (1)
x - 2y = - 9 ... (2)

(1) - 2 x (2),

(2x - y) - 2(x - 2y) = (-9) - 2(-9)

2x - y - 2x + 4y = -9 + 18

3y = 9

y = 3 ... (3)

Substitute (3) into (2),

x - 2(3) = - 9

x = -9 + 6

x = -3

The coordinates of the intersection:

x = -3
y = 3

Answer 2

if you mean the vertex of whatever conics you have passes through the intersection of the lines 2x - y = - 9 and x - 2y = -9, then, you need to solve the two equations simultaneously.

2x - y = - 9
x - 2y = - 9

multiplying 2 to the second equation

2x - y = - 9
2x - 4y = -18

and then subtracting the two equations...We have

0x + 3y = 9; or
3y = 9
y = 3

Substituting y = 3 to either of the two equations, you may find the value of x. y = 3 substituted in the first equation, we have...

2x - 3 = - 9
2x = -9 + 3
2x = -6
x = -3

If the vertex is in the form of (x,y), then it is at (-3,3)


Hope this helps...

Answer 3

these lines will intersect when they have same y value for the same x-value.
so solve for y in both, and then set the equations equal to each other and then solve for x.
2x - y = - 9
2x + 9 = y

and x - 2y = -9
x + 9 = 2y
(x+9)/2 = y

Now solve for x: 2x + 9 = (x+9)/2
2x + 9 = (x+9)/2, multiply both sides by 2
4x + 18 = x + 9
3x + 18 = 9
3x = -9
x = -3

So, when x = -3, what does y equal:
(x+9)/2 = y
(-3+9)/2 = y
6/2 = y
3 = y

2x + 9 = y
2(-3) + 9 = y
-6 + 9 = y
3 = y

So, point is (-3,3)

Answer 4

2x - y = - 9 ... (1)
x - 2y = - 9 ... (2)

(1) - 2 x (2),

(2x - y) - 2(x - 2y) = (-9) - 2(-9)

2x - y - 2x + 4y = -9 + 18

3y = 9

y = 3 ... (3)

Substitute (3) into (2),

x - 2(3) = - 9

x = -9 + 6

x = -3

The coordinates of the intersection:

x = -3
y = 3

Answer 5

2x - y = - 9
2x +9 = y


x - 2y = -9
x - 2 (2x +9) = -9
x -4x -18 = -9
-3x = 9
x = -3

-3 - 2y = -9
-2y = -6
y = 2

(-3, 2)

Answer 6

Rearrange each equasion in the form y = .............

Then solve for x, stick the figure for x in one or both of the equasions, and you'll get the value for y.