To find the point of intersection, we want to set the two equations equal to each other to find where they meet. The problem is, we have two variables, which means we can't just set them equal to each other as is. We need to manipulate the equations so that we can remove one of the variables at a time to solve for the other one.
First, let's move y to one side so we can solve for x.
2x-3y=9
2x-9=3y
y=(2x-9)/3
5x+4y=11
4y=11-5x
y=(11-5x)/4
Now that they both equal the same thing (y), we can set them equal to each other and solve for x. This will give us the x value for the point of intersection of the lines.
(11-5x)/4=(2x-9)/3
3(11-5x)=4(2x-9)
33-15x=8x-36
33+36=8x+15x
69=23x
x=69/23
x=3
Now, we can do the opposite, and solve for x to find the y coordinate.
2x-3y=9
2x=3y+9
x=(3y+9)/2
5x+4y=11
5x=11-4y
x=(11-4y)/5
(3y+9)/2=(11-4y)/5
5(3y+9)=2(11-4y)
15y+45=22-8y
15y+8y=22-45
23y= -23
y= -1
The coordinates for the point of intersection of the two lines is (3, -1).
ok consider a rectangle with two sets of equal sides
call one side of a set x
and one side of the other set y
we know she has 140 meters of rope so perimeter of the rectangle = 140
so 2x + 2y= 140
hence X = (140- 2y)/2
the dimensions have to satisfy the above equation
Answer:
154.2g
Step-by-step explanation:
This is quite straightforward, what we need to add the masses together.
113g + 114g + 27.2g = 154.2g
Answer:
x = 10
Step-by-step explanation:
Since the two triangles are congruent, ∠B ≅ ∠E
50 = 5x
x = 10
