Answer: In the equations that you have given, we have a dependent system.
2x + y = 8 (I assumed that you meant to type y instead of 7)
6x + 3y = 24
To use Cramer's Rule, we have to take the determinant of 3 different matrices written in the problem. Taking the determinant of the coefficient matrix produces a zero.
2 1 This is the coefficient matrix.
6 3
6 - 6 = 0
Since this is 0, the rest of the work will be undefined meaning the systems are dependent (or they are the versions of the same equation).
[ y - 4 = x - 8 ] is not the equation of the line that goes through
those two points. The first point (8, 4) is on the graph of that
equation, but the second point (0, 2) is not.
The slope/intercept equation of the line that passes through
both points (8, 4) and (0, 2) is
y = 1/4 x + 2 .
The slope/intercept form of [ y - 4 = x - 8 ] is
y = x - 4 .
<h3>
Answers:</h3>
The first ordered pair is ( -4 , -3 )
The second ordered pair is ( 8, 3 )
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Explanation:
The first point is (x,-3) where x is unknown. It pairs up with y = -3 so we can use algebra to find x
x-2y = 2
x-2(-3) = 2 ... replace every y with -3; isolate x
x+6 = 2
x = 2-6
x = -4
The first point is (-4, -3)
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We'll do something similar for the other point. This time we know x but don't know y. Plug x = 8 into the equation and solve for y
x-2y = 2
8-2y = 2
-2y = 2-8
-2y = -6
y = -6/(-2)
y = 3
The second point is (8, 3)
The answer is 16 outcomes, there are two possible outcomes per classroom, and there are 8 classrooms
