Find the point of intersection between y=2-(1/2)x and y=1+ax. (a=alpha sign). You answer will be a point in the xy plane whose coordinates involve the unknown a .
My work so far:
I set the two equations equal to each other because they intersect.
1+ax=2-(1/2)x
and I got,
(-1)/( (-1/2)-a )=x
how do I find y?
Do I plug in what i found for x into one of the equation? Please help!
y = 2 - x/2
y = 1 + ax
0 = 1 - x/2 - ax
x(a + 1/2) = x(2a+1)/2 = 1
x = 2/(2a+1)
y = 1 + 2a/(2a+1)
You started out OK, but should have simplified the equation for x and used it to derive an equation for y.
thank you! =D
do you have jiskha for 5th grade
To find the point of intersection between the two given equations, you've correctly set them equal to each other:
1 + ax = 2 - (1/2)x
Now, let's solve for x by simplifying the equation:
(1/2)x + (ax) = 1
Combining like terms, we have:
[(1/2) + a]x = 1
Now to isolate x, divide both sides of the equation by [(1/2) + a]:
x = 1 / [(1/2) + a]
To find the corresponding y-coordinate, we can substitute this value of x into either of the original equations. Let's use y = 2 - (1/2)x:
y = 2 - (1/2) * (1 / [(1/2) + a])
Simplifying this expression, we get:
y = 2 - 1 / (1 + 2a)
Thus, the coordinates of the point of intersection between the two equations are:
(x, y) = [1 / (1/2 + a), 2 - 1/(1 + 2a)]
Here, the value of a is the unknown parameter that determines the specific coordinates of the point.