Question 828304: 3 systems of 2 equations/inequalities y=2x+1 y= -6x y=3x+1 use each method to solve 1 system [a] graphing [b] substitution [c] elimination find a system that has each of the following coincident lines,intersecting lines,parallel lines,perpendicular lines explain reasoning
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
given:
y = 2x + 1
y = -6x
y = 3x + 1
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by observation, the three linear equations are all mutually intersecting, because they all have different slopes.
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the three equations give rise to three possible linear systems of two equations each.
I will solve one of those systems, and you can do the rest:
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y = 2x + 1
y = 3x + 1
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put the system of linear equations into standard form:
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2x - y = -1
3x - y = -1
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copy and paste the above linear system in standard form into this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution by matrix method:
x = 0
y = 1
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system matrix
2 -1
3 -1
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inverse of system matrix
-1 1
-3 2
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determinant of system matrix = 1
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now by elimination method:
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y = 2x + 1
(y = 3x + 1) * -1
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y = 2x + 1
-y = -3x + -1
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add the system:
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-x = 0
x = 0
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y = 2x + 1
y = 2(0) + 1
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y = 1
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solution by elimination method:
x = 0
y = 1
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the method agree.
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Solve quadratic equations, quadratic formula:
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Solve systems of linear equations up to 6-equations 6-variables:
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