A system of linear equations includes the line that is created by the equation y = x+ 3, graphed below, and the line through the
points (3, 1) and (4, 3).
On a coordinate plane, a line goes through (0, 3) and (2, 5).
What is the solution to the system of equations?
On a coordinate plane, a line goes through (0, 3) and (2, 5).
What is the solution to the system of equations?
1 answer:
Answer:
(8, 11)
Step-by-step explanation:
The 2-point form of the equation of a line is useful for the one where only points are given.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (3 -1)/(4 -3)(x -3) +1
y = 2(x -3) +1
We can equate this to the expression for y in the given equation.
x +3 = 2(x -3) +1
x +3 = 2x -5 . . . . . . eliminate parentheses
8 = x . . . . . . . . . . . . add 5-x
Using the given equation, we can find y:
y = x +3 = 8 +3
y = 11
The solution to the system is (x, y) = (8, 11).
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Answer:
√3 is irrational
Step-by-step explanation:
The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.
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<h3>Equilateral triangle</h3>The line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.
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cos(60°)·x + sin(60°)·y
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