PLEASE HELP ME SOLVE THIS EQUATION. 5X-2Y=-5, Y-5X=3.
THANK YOU SO MUCH. MRS. NEESE.
5X - 2Y = -5
Y - 5X = 3
Method 1: substitution:
5X - 2Y = -5
Y - 5X = 3
Solve the second equation for Y
Add +5X to both sides
Y - 5X = 3
+ 5X + 5X
--------------
Y = 3 + 5x
Now replace Y in the first equation by (3 + 5X)
5X - 2Y = -5
5X - 2(3 + 5X) = -5
Now solve it for X, First remove the parenthese:
5X - 6 - 10X = -5
-5X - 6 = -5
Add +6 to both sides
-5X = 1
Divide both sides by -5
X = -1/5
Now replace X by (-1/5) in the equation where
you solved for Y
Y = 3 + 5x
Y = 3 + 5(-1/5)
Y = 3 - 1
Y = 2
So the solution is (X, Y) = (-1/5, 2)
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Method 2: Elimination (sometimes called "addition" or
"addition and subtraction")
5X - 2Y = -5
Y - 5X = 3
Rearrange the terms of the second equation so terms in the same letter
are lined up vertically:
5X - 2Y = -5
-5X + Y = 3
Since the terms in X have coefficients which are equal in absolute
value but opposite in sign, they will cancel when added vertically:
5X - 2Y = -5
-5X + Y = 3
--------------
-Y = -2
Y = 2
To cause the Y terms to cancel, leave the first equation as is but
multiply the second equation through by 2 so that they +Y term will
become +2Y and will cancel with the -2Y above it when adding the
two equations vertically:
5X - 2Y = -5
2[-5X + Y = 3]
becomes:
5X - 2Y = -5
-10X + 2Y = 6
---------------
-5X = 1
X = -1/5
So the solution is (X, Y) = (-1/5, 2)
Edwin
AnlytcPhil@aol.com
