Answer:
(4, 3)
Step-by-step explanation:
If a point O(x, y) divides a line segment AB with end points at A(
) and B(
) in the ratio of n:m, then the location of O is at:
Given that Nates house is located at (-2,4) while the park is located at (10,2). Macs house if it is 1/2 of the distance from Nates house to the park (that is in the ratio of 1:1). Let (x, y) be the coordinate of Macs house, therefore:
The location of Macs house is (4, 3)
Let x = the first number
y = the second number
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First: set up the equations.
Four times a first number: 4x
Decreased by a second number: - y
Is 4: = 4
4x - y = 4.
The first number increased by: x +
three times the second number: 3y
is -25: = -25
x + 3y = -25.
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You can make your system of equations now.
4x - y = 4
x + 3y = -25
I would use substitution to solve these.
To do substitution, isolate a variable first, in one of the equations. I would probably isolate x in the second equation.
x + 3y = -25
x = -25 - 3y
Now, you can substitute -25 - 3y into 4x - y = 4, as x.
4x - y = 4
4(-25 - 3y) - y = 4
Now just solve for y.
-100 - 12y - y = 4
-13y = 104
y = -8
Now, you can put -8 as y into one of the original equations, I'll just use 4x - y = 4.
4x - y = 4
4x - (-8) = 4
4x + 8 = 4
4x = -4
x = -1
So the first number is -1, and the second -2.
The answer is 3. 20/2=10 10-7=3
