A system of linear equations in two variables can have _____ solutions

2 answers:

8 0

If the lines are parallel (have the same slope but different intercepts) . . .
   no solution, because they never cross.

If the lines have different slopes . . .
   one solution, because they have exactly one common point.

If the lines have the same slope and the same intercept . . .
   infinitely many solutions, because every point on one line is also a point on
   the other line, one lays right on top of the other, and when you look at them on
   the graph, it looks like only one line.

madreJ [45]3 years ago

5 0

One solution
or no solution
or an infinite number of solutions

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The slope of AB is 3 over 4 and point A is (2. 9). How many possible locations are there for point

nignag [31]

Answer:

Part 1) There are infinity locations for the point B

Part 2) see the explanation

Step-by-step explanation:

Part 1) How many possible locations are there for point B?

we know that

The equation of a line in point slope form is equal to

$y-y1=m(x-x1)$

where

$m=\frac{3}{4}$

$(x1,y1)=(2,9)$

substitute

$y-9=\frac{3}{4}(x-2)$

Convert to slope intercept form

$y-9=\frac{3}{4}x-\frac{6}{4}$

$y=\frac{3}{4}x-\frac{6}{4}+9$

$y=\frac{3}{4}x+\frac{30}{4}$

$y=0.75x+7.5$

Point B can be any point ( different from point A) that satisfies the linear equation

therefore

There are infinity locations for the point B

Part 2) Describes a method to location the point

To locate the point, one of the two coordinates must be known. The known coordinate is placed into the linear equation and the equation is solved to find the value of the missing coordinate

Example

Suppose that the x-coordinate of point B is 4

For x=4

substitute in the linear equation

$y=0.75(4)+7.5=10.5$