X - 2y = 3
<span>4x^2 - 5xy + 6y = 3
lets solve for x the first and substitute in the second:
x = 3 + 2y
4(</span>3 + 2y)^2 - 5(3 + 2y)y + 6y = 3
4(9 + 12y + 4y^2) - 15y - 10y^2 = 3
36 + 48y +16y^2<span> - 15y - </span><span>10y^2 = 3
6y^2 + 33y + 33 = 0
we can solve using the general quadratic formula:
y = (-33 +- </span>√(33^2 - 4*6*33)<span>)/12
</span>y = (-33 +- √(297)<span>)/12
</span>so there are 2 solutions for y:
y1 = (-33 + √(297)<span>)/12
</span>y2 = (-33 - √(297)<span>)/12
</span>pick one and then substitute the y value in the first equation to find x
Answer:
-11/15 is the greatest because ita in negative
Step-by-step explanation:
For two points (x₁, y₁) and (x₂, y₂), the distance between them is:
d² = (x₁ − x₂)² + (y₁ − y₂)²
The order of points 1 and 2 don't matter. You can switch it:
d² = (x₂ − x₁)² + (y₂ − y₁)²
This is basically the Pythagorean theorem for a coordinate system.
Let's do an example. If you have points (1, 2) and (4, 6), then the distance between them is:
d² = (4 − 1)² + (6 − 2)²
d² = 3² + 4²
d² = 9 + 16
d² = 25
d = 5
If you have points with negative coordinates, remember that subtracting a negative is the same as adding a positive.
For example, the distance between (-1, -2) and (4, 10) is:
d² = (4 − (-1))² + (10 − (-2))²
d² = (4 + 1)² + (10 + 2)²
d² = 5² + 12²
d² = 25 + 144
d² = 169
d = 13
