SOLUTION: compare equations with one variables to equations with two variables equations. how are they alike? how are they different? what if an equation had three unknown variables? you

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Question 29785: compare equations with one variables to equations with two variables equations.
how are they alike? how are they different?
what if an equation had three unknown variables? you would need 3 equations in order to solve them.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
compare equations with one variables to equations with two variables equations.
how are they alike? how are they different?
what if an equation had three unknown variables? you would need 3 equations in order to solve them.
I...ONE VARIABLE OR ONE UNKNOWN EQUATIONS....IN THESE EQUATIONS THERE WILL BE ONLY ONE UNKNOWN/VARIABLE TO BE FOUND.FOR THIS PURPOSE WE NEED ONE EQUATION INVOLVING THE VARIABLE...IT CAN HAVE ONE UNQUE ANSWER OR NO ANSWER OR MANY MANY INFINITE ANSWERS.....EXAMPLES
1.ONE UNIQUE SOLUTION......
X+4=5....THE ANSWER IS X=1....
2.NO SOLUTION......
X+4=X+5.....NO VALUE OF X CAN SATISFY THIS EQUATION.
3.INFINITE SOLUTIONS.....
X+4=X+4....ANY VALUE OF X SAY 1 OR 2 OR 3...OR...ANY VALUE OF X WILL SATISFY THIS EQUATION.
II...TWO VARIABLES OR TWO UNKNOWNS EQUATIONS....IN THESE EQUATIONS THERE WILL BE TWO UNKNOWNS/VARIABLES TO BE FOUND...FOR THIS PURPOSE WE NEED TWO EQUATIONS INVOLVING THE TWO VARIABLES.IT CAN HAVE ONE UNQUE ANSWER OR NO ANSWER OR MANY MANY INFINITE ANSWERS.....EXAMPLES
1.ONE UNIQUE SOLUTION......
X+Y=5....
X-Y=1
THE ANSWER IS X=3 AND Y=2....
2.NO SOLUTION......
X+Y=5.....
2X+2Y=8....
NO SINGLE SET OF VALUES OF X & Y CAN SATISFY THESE TWO EQUATIONS.
3.INFINITE SOLUTIONS.....
X+Y=5....
2X+2Y=10....
MANY SETS OF VALUES OF X AND Y SAY X=1 AND Y=4 OR X=2 AND Y=3 OR X=3 AND Y=2...OR...MANY MANT OR INFINITE SETS OF VALUES OF X AND Y WILL SATISFY THESE EQUATIONS.
III...THREE VARIABLES OR THREE UNKNOWNS EQUATIONS....IN THESE EQUATIONS THERE WILL BE THREE UNKNOWNS/VARIABLES TO BE FOUND...FOR THIS PURPOSE WE NEED THREE EQUATIONS INVOLVING THE THREE VARIABLES..IT CAN HAVE ONE UNQUE ANSWER OR NO ANSWER OR MANY MANY INFINITE ANSWERS.....EXAMPLES
WHY SOME HAVE ONE UNIQUE SOLUTION ,WHILE SOME OTHERS HAVE NO SOLUTION OR INFINITE SOLUTIONS IS A WIDER TOPIC FOR STUDY AND DEPENDING ON YOUR COURSE OF STUDY WE CAN DEAL WITH THEM...