LINEAR EQUATIONS AND THEIR SOLUTIONS Flashcards
WHAT DOES AN ARITHMETICAL QUANTITY HAVE?
A DEFINITE VALUE
93 OR 3.77
WHAT DOES AN ALGEBRAIC QUANTITY REPRESENT?
ANY AMOUNT DEPENDING ON THE VALUE GIVEN TO A VARIABLE (SUCH AS x)
WHAT ARE THE TWO METHODS IN ALGEBRA TO SHOW THAT TWO QUANTITIES ARE EQUIVALENT TO EACH OTHER?
- EQUATION
- IDENTITY
WHAT DOES EQUATION MEAN WITH REFERENCE TO SHOW HOW TWO QUANTITIES ARE EQUIVALENT TO EACH OTHER?
A MATHEMATICAL STATEMENT THAT SHOWS THAT TWO AMOUNTS ARE EQUAL USING MATHEMATICAL SYMBOLS.
x + 3 = 5 | THERE IS ONLY ONE VALUE OF x THAT WILL SATISFY THE EQUATION.
WHAT DOES IDENTITY MEAN WITH REFERENCE TO SHOW HOW TWO QUANTITIES ARE EQUIVALENT TO EACH OTHER?
AN EQUATION THAT IS TRUE NO MATTER WHAT VALUES ARE CHOSEN.
3x + 2x = 5x | IS AN IDENTITY, BECAUSE TWO SIDES ARE EQUAL FOR VALUE x.
WHAT IS IMPORTANT TO NOTE ABOUT THE LHS AND THE RHS OF AN EQUATION IN ALGEBRA?
THE QUANTITY ON THE LHS IS EQUAL TO THE QUANTITY ON THE RHS.
WHAT DO LINEAR EQUATIONS CONTAIN?
LINEAR EQUATIONS CONTAIN ONLY THE FIRST POWER OF THE UNKNOWN QUANTITY.
TO THE POWER OF ONE | 7t - 5 = 4t +7
SOLVING LINEAR EQUATIONS
REGARDLESS OF HOW THE APPEARANCE OF A LINEAR EQUATION ALTERS WHAT MUST YOU BE MINDFUL OF?
THE VALUES ON BOTH SIDES MUST REMAIN EQUAL TO EACH OTHER.
SOLVING LINEAR EQUATIONS
HOW CAN WE PRESERVE THE EQUALITY OF THE LINEAR EQUATION?
WHATEVER IS DONE TO ONE SIDE OF THE EQUATION MUST BE DONE TO THE OTHER SIDE.
SOLVING LINEAR EQUATIONS
WHAT IS THE FIRST RULE OF LINEAR EQUATIONS?
ALWAYS DO THE SAME THING MATHEMATICALLY TO BOTH SIDES OF THE EQUATION.
SOLVING LINEAR EQUATIONS
WHAT IS THE SECOND RULE OF LINEAR EQUATIONS?
TO GET RID OF SOMETHING DO THE OPPOSITE.
THE OPPOSITE OF + IS -
THE OPPOSITE OF - IS +
THE OPPOSITE OF x IS /
THE OPPOSITE OF / IS x
SOLVING LINEAR EQUATIONS
WHAT IS THE THIRD RULE OF LINEAR EQUATIONS?
CONTINUE UNTIL YOU HAVE THE LETTER THAT YOU WANT ON ITS OWN (SUBJECT OF THE FORMULA)
EQUATIONS REQUIRING ADDITION AND SUBTRACTION
HOW CAN YOU CHECK A SOLUTION THAT HAS BEEN SOLVED THAT IT IS CORRECT?
- SUBSTITUTING THE RESULT IN EACH SIDE OF THE EQUATION SEPARATELY.
- IF EACH SIDE OF THE EQUATION HAS THE SAME VALUE THE SOLUTION IS CORRECT.
EQUATIONS REQUIRING MULTIPLICATION AND DIVISION
HOW CAN YOU CHECK A SOLUTION THAT HAS BEEN SOLVED THAT IT IS CORRECT?
- SUBSTITUTING THE RESULT IN EACH SIDE OF THE EQUATION SEPARATELY.
- IF EACH SIDE OF THE EQUATION HAS THE SAME VALUE THE SOLUTION IS CORRECT.
EQUATIONS CONTAINING AN UNKNOWN QUANTITY ON BOTH SIDES
WHAT MUST YOU DO WHEN SOLVING EQUATIONS WITH UNKNOWN QUANTITIES ON BOTH SIDES?
- GROUP ALL TERMS CONTAINING THE UNKNOWN QUANTITY ON ONE SIDE OF THE EQUATION
- GROUP ALL REMAINING TERMS ON THE OTHER SIDE
