SOLVING EQUATIONS : CALCULATOR Equivalent Equation - All terms on left side : right side = 0 "City Streets" X-Intercept X-Intercept X-Intercept X-Intercept Intersection Intersection Intersection Intersection Intersection Balance Value Y 1 = left side Y 1 = Equation Y 1 = Equation Y 1 = Equation Y 1 = Equation Y 2 = right side Y 2 = 0 (x-axis) Graph Screen Graph Screen Graph Screen Table Screen Graph Screen #5 Intersection #5 Intersection TRACE TABLE #2 Zero x = balance value x = x-axis value x = x-axis value x = x-axis value x = x-axis value y = balance weight y = 0 y = 0 y = 0 y = 0 balance weight TRACE TABLE is amount each side of eq. only for integer think CHECK values of "X" Non-Graphing Method Table Table SOLVER Y 1 = Y 2 Y 1 = Y 2 = 0 determine X when y = 0
An equation is a "balanced statement." To solve an equation using the calculator in a graphing sense, consider a map of city streets. Two streets occupy the same space at an intersection. Y 1 Let each side of the equation be one of the streets. Street 1 The solution to the equation will be where each side Street 2 intersects with the other graphically. Y 2 Given the equation 3 x + 2 = 8 Let Y 1 be the left side of the equation Let Y 2 be the right side of the equation to enter each part of the equation Next to Y 1 = type 3x + 2 Next to Y 2 = type 8 Zoom #6 Standard for a standard graph screen In order to complete the following steps involved in solving the equation YOU MUST BE ABLE TO SEE THE POINT OF INTERSECTION ON THE GRAPH SCREEN Note: INSTRUCTIONS for what to do if you cannot see the point of intersection are on the back. *** GRAPH to view the point of intersection. 2nd TRACE for CALC Y 2 = 8 # 5 for INTERSECTION Y 1 = 3x + 2 - - is the solution 2 the value that balances both sides of the equation is the weight of each side of the equation ( X, Y ) 8
Given the equation 3 x + 2 = 2 x + 6 Let Y 1 be the left side of the equation Let Y 2 be the right side of the equation to enter each part of the equation Next to Y 1 = type 3x + 2 Next to Y 2 = type 2x + 6 Zoom #6 Standard for a standard graph screen *** What to do if you CANNOT SEE the point of intersection. Pt. of Int. Q1 Determine which Quadrant Y max the point of intersection will be in. Q2 Q1 X min X max Y 2 = 2x + 6 Q3 Q4 Y min WINDOW to adjust the graph screen Adjust the WINDOW values accordingly. Y 1 = 3x + 2 X max Graph to view the point of intersection. Y max 2nd TRACE for CALC # 5 for INTERSECTION solution is - - weight is 4 14
two streets that meet form an INTERSECTION Balance Value X-Intercept Y 1 = left side of original equation Y 1 = ALL TERMS on left side Y 2 = right side of original equation Y 2 = 0 ( x-axis ) 2nd TRACE [ CALC ] # 5 INTERSECT ( Adjust WINDOW ) ( Move CURSOR )
two streets that meet form an INTERSECTION TABLE Balance Value X-Intercept Y 1 = left side of original equation Y 1 = ALL TERMS on left side Y 2 = right side of original equation Y 2 = 0 ( x-axis ) Alternative Method : Solution - Integer X Value Only 2nd GRAPH [ TABLE ] Scroll Search for Y 1 = Y 2 Scroll Search for Y 1 = Y 2 = 0 Balance Value the value that makes equation equal to ZERO x-intercept
two streets that meet form an INTERSECTION Alternative Method : Solution - Integer X Value Only X-Intercept TRACE Y 1 = ALL TERMS on left side TRACE Type Value of X where graph crosses X-Axis For X to be a SOLUTION 0 Reapeat if Necessary
graph crosses x-axis and forms an X-INTERCEPT X-Intercept ZERO Y 1 = ALL TERMS on left side 2nd TRACE for CALC Type 2 on keypad for ZERO Move CURSOR to the LEFT of where graph crossess X-AXIS Move CURSOR to the Right of where graph crossess X-AXIS Move CURSOR close to the perceived X-INTERCEPT For X to be a SOLUTION 0
graph crosses x-axis and forms an X-INTERCEPT X-Intercept SOLVER Y 1 = ALL TERMS on left side GRAPH Estimate the X-INTERCEPT MATH UP ARROW for SOLVER VARS scroll right for Y-VARS for FUNCTION for Y 1 DOWN ARROW for SOLVER SCREEN Type Estimated X-INTERCEPT ALPHA For X to be a SOLUTION left-right = 0